已经有一个帐户?据一种href="//www.parkandroid.com/account/login/?next=/wiki/ring-theory/" class="ax-click" data-ax-id="clicked_signup_modal_login" data-ax-type="link">在此登录。据/一种>
贡献据/D.一世v>
一种据strong>戒指据/strong>是一套据span class="katex">
R.据/span>一起与两项操作据span class="katex">
(据/span>+据/span>)据/span>和据span class="katex">
(据/span>⋅据/span>)据/span>满足以下属性(环形公理):据/P.>
(1)据span class="katex">
R.据/span>是一个据一种href="//www.parkandroid.com/wiki/group-theory-introduction/" class="wiki_link" title="阿贝利亚集团" target="_blank">阿贝利亚集团据/一种>另外。那是,据span class="katex">
R.据/span>在此后关闭,有一种添加剂标识(称为据span class="katex">
0.据/span>),每个元素据span class="katex">
一种据/span>∈据/span>R.据/span>有一种添加剂逆据span class="katex">
-据/span>一种据/span>∈据/span>R.据/span>此外,加法是关联和换向。据/P.>
(2)据span class="katex">
R.据/span>在乘法下关闭,乘法是关联的:据span class="katex-display">
∀据/span>一种据/span>那据/span>B.据/span>∀据/span>一种据/span>那据/span>B.据/span>那据/span>C据/span>∈据/span>R.据/span>∈据/span>R.据/span>一种据/span>⋅据/span>B.据/span>一种据/span>⋅据/span>(据/span>B.据/span>⋅据/span>C据/span>)据/span>∈据/span>R.据/span>=据/span>(据/span>一种据/span>⋅据/span>B.据/span>)据/span>⋅据/span>C据/span>。据/span>
(3)乘法分布过量:据span class="katex-display">
∀据/span>一种据/span>那据/span>B.据/span>那据/span>C据/span>∈据/span>R.据/span>一种据/span>⋅据/span>(据/span>B.据/span>+据/span>C据/span>)据/span>=据/span>一种据/span>⋅据/span>B.据/span>+据/span>一种据/span>⋅据/span>C据/span>和据/span>(据/span>B.据/span>+据/span>C据/span>)据/span>⋅据/span>一种据/span>=据/span>B.据/span>⋅据/span>一种据/span>+据/span>C据/span>⋅据/span>一种据/span>。据/span>
戒指通常由据span class="katex">
(据/span>R.据/span>那据/span>+据/span>那据/span>⋅据/span>)据/span>而且通常它只是写作据span class="katex">
R.据/span>当操作被理解时。据span class="katex">
□据/span>
笔记:据/strong>
(1)有两种进一步的要求可能施加在戒指上据span class="katex">
S.据/span>这导致有趣的戒指。例如,如果乘法是换向的,则戒指称为a据strong>换向戒指据/strong>。换向戒指理论与非换向环理论相差得多;更好地理解换向环,并更广泛地研究过。这个Wiki的大多数例子和结果都是用于换向环。同样可能有一个元素据span class="katex">
1据/span>在据span class="katex">
R.据/span>这对于所有元素来说据span class="katex">
一种据/span>在据span class="katex">
R.据/span>那据span class="katex">
一种据/span>⋅据/span>1据/span>=据/span>1据/span>⋅据/span>一种据/span>=据/span>一种据/span>。如果存在这样的元素,我们将其称为环的统一,并且戒指称为一个据strong>圆环统一据/strong>。否则它被称为没有团结的戒指或“rng”(一个戒指没有据span class="katex">
一世据/span>)。据/P.>
(2)如果据span class="katex">
R.据/span>是一种换向戒指和据span class="katex">
一种据/span>那据/span>B.据/span>那据/span>C据/span>∈据/span>R.据/span>这样据span class="katex">
一种据/span>那据/span>B.据/span>据/span>=据/span>0.据/span>和据span class="katex">
一种据/span>⋅据/span>B.据/span>=据/span>C据/span>, 然后据span class="katex">
一种据/span>和据span class="katex">
B.据/span>据说是分类的据span class="katex">
C据/span>。如果在换向戒指中据span class="katex">
R.据/span>有了一个统一,没有添加剂标识的除法,即据span class="katex">
0.据/span>, 然后据span class="katex">
R.据/span>据说是一个据strong>积分域名据/strong>。因此是一种换向戒指据span class="katex">
R.据/span>如果所有元素,则据说统一是一个积分域据span class="katex">
一种据/span>那据/span>B.据/span>在据span class="katex">
R.据/span>那据span class="katex">
一种据/span>⋅据/span>B.据/span>=据/span>0.据/span>意思是据span class="katex">
一种据/span>=据/span>0.据/span>要么据span class="katex">
B.据/span>=据/span>0.据/span>。据/P.>
(3)如果具有统一的换向环中的每个非零元素也具有乘法反转,则戒指称为据一种href="//www.parkandroid.com/wiki/field-theory/" class="wiki_link" title="场地" target="_blank">场地据/一种>。字段是基本对象据一种href="//www.parkandroid.com/wiki/number-theory/" class="wiki_link" title="数字论" target="_blank">数字论据/一种>那据一种href="//www.parkandroid.com/wiki/algebraic-geometry/" class="wiki_link" title="代数几何" target="_blank">代数几何据/一种>以及许多其他数学领域。如果带有Unity的圆环中的每个非零元素具有乘法反转,则响铃称为a据strong>分区戒指据/strong>或者据strong>歪斜的田野据/strong>。因此,一个字段是一种换向歪曲场。非换向性被称为严格歪曲的字段。据/P.>
正常子组的模拟据一种href="//www.parkandroid.com/wiki/group-theory-introduction/" class="wiki_link" title="小组理论" target="_blank">小组理论据/一种>原来是据em>理想据/em>在戒指中。这些是允许概括的物体据一种href="//www.parkandroid.com/wiki/modular-arithmetic/" class="wiki_link" title="模块化算术" target="_blank">模块化算术据/一种>在整数上。据/P.>
在本节中,为了简单起见,所有环都将被认为是换向的。(对非换向环有这些想法的概括,但定义更笨拙。)据/P.>
一个据strong>理想的据/strong>
一世据/span>在换向戒指中据span class="katex">
R.据/span>是一个巨型的集合据/P.>
(1)在此外关闭据B.R.>(2)“吞下”乘法下的“吞下”:如果据span class="katex">
R.据/span>∈据/span>R.据/span>和据span class="katex">
一种据/span>∈据/span>一世据/span>, 然后据span class="katex">
R.据/span>一种据/span>∈据/span>一世据/span>。据/P.>
如果据span class="katex">
一种据/span>1据/span>那据/span>一种据/span>2据/span>那据/span>......据/span>那据/span>一种据/span>N.据/span>∈据/span>R.据/span>,集合据span class="katex-display">
(据/span>一种据/span>1据/span>那据/span>一种据/span>2据/span>那据/span>......据/span>那据/span>一种据/span>N.据/span>)据/span>=据/span>{据/span>R.据/span>1据/span>一种据/span>1据/span>+据/span>R.据/span>2据/span>一种据/span>2据/span>+据/span>⋯据/span>+据/span>R.据/span>N.据/span>一种据/span>N.据/span>:据/span>R.据/span>一世据/span>∈据/span>R.据/span>}据/span>是一个理想的,被称为据em>由此产生的理想据/em>
一种据/span>一世据/span>。据span class="katex">
□据/span>
理想最初是作为戒指元素的概括,以恢复一种形式据一种href="//www.parkandroid.com/wiki/fundamental-theorem-of-arithmetic/" class="wiki_link" title="独特的分解" target="_blank">独特的分解据/一种>;有关详细信息,请参阅Wiki据一种href="//www.parkandroid.com/wiki/algebraic-number-theory/" class="wiki_link" title="代数数字理论" target="_blank">代数数字理论据/一种>。据/P.>
由一个元素产生的理想,据span class="katex">
(据/span>一种据/span>)据/span>,这组倍数据span class="katex">
一种据/span>,被称为a据strong>主要理想据/strong>。一个戒指,每个理想是校长都被称为a据strong>主要理想戒指据/strong>。据span class="katex">
□据/span>
显示据span class="katex">
Z.据/span>是一个主要的理想环。据/P.>
如果据span class="katex">
K.据/span>是一个领域,表明了这一点据span class="katex">
K.据/span>[据/span>X据/span>]据/span>是一个主要的理想环。据/P.>
显示据span class="katex">
Z.据/span>[据/span>X据/span>]据/span>不是主要的理想环。据/P.>
部分解决方案:据/strong>任何合理的戒指据一种href="//www.parkandroid.com/wiki/division-algorithm/" class="wiki_link" title="划分算法" target="_blank">划分算法据/一种>被称为A.据strong>欧几里德戒指据/strong>(之后据一种href="//www.parkandroid.com/wiki/euclidean-algorithm/" class="wiki_link" title="欧几里德算法" target="_blank">欧几里德算法据/一种>)。所有这些环都是主要的理想环;这个想法是采取“最小”非零元素据span class="katex">
一种据/span>在理想中,然后使用该划分算法来显示每个其他元素据span class="katex">
B.据/span>在理想中是一个倍数据span class="katex">
一种据/span>。这是因为如果据span class="katex">
B.据/span>=据/span>一种据/span>问:据/span>+据/span>R.据/span>在哪里据span class="katex">
R.据/span>小于据span class="katex">
一种据/span>, 然后据span class="katex">
R.据/span>是理想的,但小于据span class="katex">
一种据/span>,所以必须是据span class="katex">
0.据/span>。自从据span class="katex">
Z.据/span>和据span class="katex">
K.据/span>[据/span>X据/span>]据/span>两者都有分部算法,前两种结果跟随。据span class="katex">
□据/span>
在据span class="katex">
Z.据/span>[据/span>X据/span>]据/span>, 理想据span class="katex">
(据/span>2据/span>那据/span>X据/span>)据/span>不是校长。(为读者练习。提示:考虑发电机的程度。)据/P.>
给予戒指据span class="katex">
R.据/span>和一个理想的据span class="katex">
一世据/span>,有一个名为的对象据strong>商戒指据/strong>
R.据/span>/据/span>一世据/span>。要记住的例子是据span class="katex">
R.据/span>=据/span>Z.据/span>和据span class="katex">
一世据/span>=据/span>由整数产生的理想据span class="katex">
N.据/span>。然后据span class="katex">
R.据/span>/据/span>一世据/span>=据/span>Z.据/span>/据/span>(据/span>N.据/span>)据/span>是熟悉的整数mod的环据span class="katex">
N.据/span>。据/P.>
戒指据span class="katex">
R.据/span>/据/span>一世据/span>是一组元素据span class="katex">
一种据/span>, 在哪里据span class="katex">
一种据/span>∈据/span>R.据/span>。两个表达据span class="katex">
一种据/span>和据span class="katex">
B.据/span>等于据span class="katex">
R.据/span>/据/span>一世据/span>如果并且只有据span class="katex">
一种据/span>-据/span>B.据/span>∈据/span>一世据/span>。元素被添加并乘以它们据span class="katex">
R.据/span>:据span class="katex">
一种据/span>+据/span>B.据/span>=据/span>一种据/span>+据/span>B.据/span>和据span class="katex">
一种据/span>⋅据/span>B.据/span>=据/span>一种据/span>B.据/span>。据span class="katex">
□据/span>
本定义的微妙部分是它是明确的:也就是说,算术据span class="katex">
R.据/span>/据/span>一世据/span>无论代表性如何,都提供了同样的结果据span class="katex">
一种据/span>元素据span class="katex">
一种据/span>被选中。(再次,牢记的例子是据span class="katex">
Z.据/span>/据/span>(据/span>N.据/span>)据/span>。)这个井清晰度的证据用来以必要的方式使用理想的属性(并留下作为读者的练习)。据/P.>
如果据span class="katex">
R.据/span>=据/span>Z.据/span>和据span class="katex">
一世据/span>=据/span>(据/span>N.据/span>)据/span>, 然后据span class="katex">
R.据/span>/据/span>一世据/span>=据/span>Z.据/span>/据/span>(据/span>N.据/span>)据/span>早些时候评论过。据/P.>
如果据span class="katex">
R.据/span>=据/span>Z.据/span>[据/span>X据/span>]据/span>和据span class="katex">
一世据/span>=据/span>(据/span>X据/span>2据/span>-据/span>2据/span>)据/span>, 然后据span class="katex">
R.据/span>/据/span>一世据/span>可以识别据span class="katex">
Z.据/span>[据/span>2据/span>
]据/span>,通过识别据span class="katex">
X据/span>和据span class="katex">
2据/span>
。(注意据span class="katex">
X据/span>2据/span>=据/span>X据/span>2据/span>=据/span>X据/span>2据/span>-据/span>(据/span>X据/span>2据/span>-据/span>2据/span>)据/span>=据/span>2据/span>在据span class="katex">
R.据/span>/据/span>一世据/span>, 所以据span class="katex">
X据/span>是一个平方根据span class="katex">
2据/span>。)据!-- end-example -->
如果据span class="katex">
R.据/span>=据/span>Z.据/span>[据/span>X据/span>]据/span>和据span class="katex">
一世据/span>=据/span>(据/span>X据/span>2据/span>+据/span>1据/span>)据/span>, 然后据span class="katex">
R.据/span>/据/span>一世据/span>可以识别据一种href="//www.parkandroid.com/wiki/gaussian-integers/" class="wiki_link" title="高斯整数" target="_blank">高斯整数据/一种>那据span class="katex">
Z.据/span>[据/span>一世据/span>]据/span>,通过识别据span class="katex">
X据/span>和据span class="katex">
一世据/span>。据/P.>
如果据span class="katex">
一种据/span>B.据/span>=据/span>0.据/span>在据span class="katex">
R.据/span>和据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是非零,然后是据span class="katex">
一种据/span>和据span class="katex">
B.据/span>被称为据strong>零除数据/strong>。没有零除数的戒指被称为据strong>领域据/strong>,和换向域名被称为据strong>积分域名据/strong>。据/P.>
对于那么据span class="katex">
N.据/span>≥据/span>2据/span>是据span class="katex">
Z.据/span>/据/span>(据/span>N.据/span>)据/span>一个积分域名?据/P.>
如果据span class="katex">
N.据/span>=据/span>一种据/span>B.据/span>是复合物(哪里据span class="katex">
1据/span>据据/span>一种据/span>那据/span>B.据/span>据据/span>N.据/span>), 然后据span class="katex">
一种据/span>B.据/span>≡据/span>0.据/span>摩擦据span class="katex">
N.据/span>但据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是非零mod.据span class="katex">
N.据/span>因为它们严格小于据span class="katex">
N.据/span>。所以据span class="katex">
Z.据/span>/据/span>(据/span>N.据/span>)据/span>不是一个积分域时据span class="katex">
N.据/span>是综合。据/P.>
另一方面,如果据span class="katex">
N.据/span>是素质和据span class="katex">
一种据/span>B.据/span>≡据/span>0.据/span>摩擦据span class="katex">
N.据/span>, 然后据span class="katex">
N.据/span>|据/span>一种据/span>B.据/span>, 所以据span class="katex">
N.据/span>|据/span>一种据/span>要么据span class="katex">
N.据/span>|据/span>B.据/span>因为据span class="katex">
N.据/span>是素数。所以那就是据span class="katex">
一种据/span>要么据span class="katex">
B.据/span>是据span class="katex">
0.据/span>摩擦据span class="katex">
N.据/span>。所以据span class="katex">
Z.据/span>/据/span>(据/span>N.据/span>)据/span>是一个积分域时据span class="katex">
N.据/span>是素数。据span class="katex">
□据/span>
积分域条件弱于现场条件:据/P.>
每个字段都是一个积分域,但不是每个整体域都是一个字段。据/P.>
首先有一个据strong>引理:据/strong>对于所有元素据span class="katex">
一种据/span>戒指据span class="katex">
R.据/span>那据span class="katex">
一种据/span>⋅据/span>0.据/span>=据/span>0.据/span>⋅据/span>一种据/span>=据/span>0.据/span>。据/P.>
lemma证明:据/strong>自从据span class="katex">
0.据/span>是添加剂身份,据span class="katex">
0.据/span>+据/span>0.据/span>=据/span>0.据/span>。然后据span class="katex">
一种据/span>⋅据/span>0.据/span>+据/span>一种据/span>⋅据/span>0.据/span>=据/span>一种据/span>⋅据/span>0.据/span>通过分配法。但我们可以添加添加剂逆据span class="katex">
一种据/span>⋅据/span>0.据/span>到双方,得到据span class="katex">
一种据/span>⋅据/span>0.据/span>=据/span>0.据/span>。证明据span class="katex">
0.据/span>⋅据/span>一种据/span>很相似。据/P.>
现在是为了证明结果。如果每个非零元素都有乘法反转,假设据span class="katex">
一种据/span>B.据/span>=据/span>0.据/span>但据span class="katex">
一种据/span>和据span class="katex">
B.据/span>是非零的。然后乘以双方据span class="katex">
一种据/span>-据/span>1据/span>要得到据span class="katex">
一种据/span>-据/span>1据/span>一种据/span>B.据/span>=据/span>一种据/span>-据/span>1据/span>0.据/span>=据/span>0.据/span>那据/span>所以据span class="katex">
B.据/span>=据/span>0.据/span>那据/span>矛盾。所以没有零除数。据/P.>
要看到不是每个整体域都是一个字段,只需注意到据span class="katex">
Z.据/span>是不是字段的积分域的一个例子(自如此以来。据span class="katex">
2据/span>没有乘法反转据span class="katex">
Z.据/span>)。据span class="katex">
□据/span>
一个理想的据span class="katex">
一世据/span>戒指据span class="katex">
R.据/span>是据strong>鼎盛时期据/strong>如果据span class="katex">
一世据/span>据/span>=据/span>R.据/span>和据span class="katex">
一种据/span>B.据/span>∈据/span>一世据/span>⇒据/span>一种据/span>∈据/span>一世据/span>要么据span class="katex">
B.据/span>∈据/span>一世据/span>。据/P.>
一个理想的据span class="katex">
一世据/span>戒指据span class="katex">
R.据/span>是据strong>最大据/strong>如果据span class="katex">
一世据/span>据/span>=据/span>R.据/span>但任何严格含有的理想据span class="katex">
一世据/span>是整个戒指据span class="katex">
R.据/span>。(即理想的是据span class="katex">
j据/span>那据span class="katex">
一世据/span>⊆据/span>j据/span>⊆据/span>R.据/span>暗示据span class="katex">
一世据/span>=据/span>j据/span>要么据span class="katex">
j据/span>=据/span>R.据/span>。)据span class="katex">
□据/span>
理想据span class="katex">
(据/span>3.据/span>)据/span>的据span class="katex">
Z.据/span>是素数,因为如果据span class="katex">
一种据/span>B.据/span>∈据/span>(据/span>3.据/span>)据/span>, 然后据span class="katex">
3.据/span>|据/span>一种据/span>B.据/span>, 所以据span class="katex">
3.据/span>|据/span>一种据/span>要么据span class="katex">
3.据/span>|据/span>B.据/span>(因为据span class="katex">
3.据/span>是一个素数),所以据span class="katex">
一种据/span>∈据/span>(据/span>3.据/span>)据/span>要么据span class="katex">
B.据/span>∈据/span>(据/span>3.据/span>)据/span>。据/P.>
它也是最大的,因为如果据span class="katex">
j据/span>是一个非常含有的理想据span class="katex">
一世据/span>,然后有一个元素据span class="katex">
j据/span>∈据/span>j据/span>那不是倍数据span class="katex">
3.据/span>。现在,自以来据span class="katex">
GCD.据/span>(据/span>3.据/span>那据/span>j据/span>)据/span>=据/span>1据/span>, 有据span class="katex">
X据/span>那据/span>y据/span>∈据/span>Z.据/span>这样据span class="katex">
3.据/span>X据/span>+据/span>j据/span>y据/span>=据/span>1据/span>经过据一种href="//www.parkandroid.com/wiki/bezouts-identity/" class="wiki_link" title="Bezout的身份" target="_blank">Bezout的身份据/一种>, 但据span class="katex">
3.据/span>X据/span>和据span class="katex">
j据/span>y据/span>都是据span class="katex">
j据/span>,所以他们的总和是,所以据span class="katex">
1据/span>∈据/span>j据/span>。据/P.>
但随后据span class="katex">
R.据/span>∈据/span>R.据/span>那据span class="katex">
R.据/span>=据/span>1据/span>⋅据/span>R.据/span>是据span class="katex">
j据/span>, 所以据span class="katex">
j据/span>=据/span>R.据/span>。据/P.>
另一方面,据span class="katex">
(据/span>4.据/span>)据/span>既不是素数也不是最大的,因为据span class="katex">
2据/span>⋅据/span>2据/span>∈据/span>(据/span>4.据/span>)据/span>但据span class="katex">
2据/span>∈据/span>/据/span>(据/span>4.据/span>)据/span>;和理想据span class="katex">
(据/span>2据/span>)据/span>严格大于据span class="katex">
(据/span>4.据/span>)据/span>但不是整个戒指。据/P.>
这是一个很好的定理,将一些来自这个维基的概念联系在一起。据/P.>
让据span class="katex">
R.据/span>是一个换向戒指,让据span class="katex">
一世据/span>是一个不等于的理想据span class="katex">
R.据/span>。然后:据/P.>
(1)据span class="katex">
R.据/span>/据/span>一世据/span>如果才是仅当且仅当据span class="katex">
一世据/span>是素质据B.R.>(2)据span class="katex">
R.据/span>/据/span>一世据/span>如果且仅当据span class="katex">
一世据/span>最大值。据span class="katex">
□据/span>
(1)直接来自定义:如果据span class="katex">
R.据/span>/据/span>一世据/span>是一个积分域和据span class="katex">
一种据/span>B.据/span>∈据/span>一世据/span>, 然后据span class="katex">
一种据/span>B.据/span>=据/span>0.据/span>在据span class="katex">
R.据/span>/据/span>一世据/span>, 所以据span class="katex">
一种据/span>=据/span>0.据/span>要么据span class="katex">
B.据/span>=据/span>0.据/span>, 所以据span class="katex">
一种据/span>∈据/span>一世据/span>要么据span class="katex">
B.据/span>∈据/span>一世据/span>, 所以据span class="katex">
一世据/span>是素数。交谈类似。据/P.>
对于(2),假设据span class="katex">
一世据/span>是最大的;然后拿一个非零元素据span class="katex">
一种据/span>∈据/span>R.据/span>/据/span>一世据/span>。然后据span class="katex-display">
(据/span>一种据/span>那据/span>一世据/span>)据/span>=据/span>{据/span>一种据/span>X据/span>+据/span>一世据/span>:据/span>X据/span>∈据/span>R.据/span>那据/span>一世据/span>∈据/span>一世据/span>}据/span>是一个理想的,它严格大于据span class="katex">
一世据/span>因为它包含据span class="katex">
一种据/span>∈据/span>/据/span>一世据/span>。所以它必须等于整个戒指据span class="katex">
R.据/span>,特别是它包含据span class="katex">
1据/span>。据/P.>
所以存在据span class="katex">
X据/span>0.据/span>∈据/span>R.据/span>那据/span>一世据/span>0.据/span>∈据/span>一世据/span>这样据span class="katex">
一种据/span>X据/span>0.据/span>+据/span>一世据/span>0.据/span>=据/span>1据/span>,在据span class="katex">
R.据/span>/据/span>一世据/span>这成为了据span class="katex-display">
一种据/span>X据/span>0.据/span>=据/span>1据/span>那据/span>所以据span class="katex">
一种据/span>有一个乘法反转据span class="katex">
R.据/span>/据/span>一世据/span>。这表明了据span class="katex">
R.据/span>/据/span>一世据/span>是一个领域。交谈类似。据span class="katex">
□据/span>
请注意,此目前显示每个最大理想是素质,由前一节的结果。据/P.>
1据/span>
无限很多据/span>
2据/span>
0.据/span>
一个非空的集合据span class="katex">
一世据/span>在戒指中据span class="katex">
R.据/span>被称为A.据strong>理想的据/strong>如果据/P.>
(1)它未完成补充:据span class="katex">
一种据/span>∈据/span>一世据/span>那据/span>B.据/span>∈据/span>一世据/span>⇒据/span>一种据/span>+据/span>B.据/span>∈据/span>一世据/span>
(2)乘法下的“吞下”:据span class="katex">
一种据/span>∈据/span>R.据/span>那据/span>一世据/span>∈据/span>一世据/span>⇒据/span>一种据/span>一世据/span>∈据/span>一世据/span>。据/P.>
一种据strong>适当的理想据/strong>是一个不等于整个环的一个。据/P.>
适当的理想是据strong>鼎盛时期据/strong>如果据span class="katex">
一种据/span>B.据/span>∈据/span>一世据/span>暗示据span class="katex">
一种据/span>∈据/span>一世据/span>要么据span class="katex">
B.据/span>∈据/span>一世据/span>。据/P.>
适当的理想是据strong>最大据/strong>如果它和整个环之间没有理想:如果据span class="katex">
j据/span>那是一个理想的,然后据span class="katex">
一世据/span>⊆据/span>j据/span>⊆据/span>R.据/span>暗示据span class="katex">
一世据/span>=据/span>j据/span>要么据span class="katex">
j据/span>=据/span>R.据/span>。据/P.>
有多少理想据span class="katex">
Z.据/span>是素质但不是最大的?据/P.>
它应该有助于阅读环理论维基!据/h6>
引用如下:据/strong>环理论。据em>bright.org.据/em>。检索到据span class="retrieval-time">从据一种href="//www.parkandroid.com/wiki/ring-theory/">//www.parkandroid.com/wiki/ring-theory/据/一种>