| 环的B-稳定正则理想 |
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| 引用本文： | 陈焕艮.环的B-稳定正则理想[J].数学年刊A辑(中文版),2012,33(1):123-132. |
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| 作者姓名： | 陈焕艮 |
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| 作者单位： | 杭州师范大学数学系 |
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| 基金项目： | 浙江省自然科学基金(No.Y6090404);杭州师范大学科研基金(No.200901)资助的项目 |
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| 摘 要： | 研究了正则理想是B-稳定的充分和必要条件,并且证明环R的正则理想I是B-稳定的当且仅当对任意的有限生成投射右R-模A,如果A1和A2是A的有限生成子模且满足A1≌A2,A1=A1I以及A2=A2I,则存在一个有限生成子模B,使得A=A1（?）B=A2（?）B;当且仅当对任意的幂等元e,f∈I,eR≌fR蕴含eR/（eR∩fR）≌fR/（eR∩fR）;当且仅当对任意的a∈1+I,存在一个幂等元e∈I,使得a-e∈∪（R）并且aR∩eR=0.进而构造了相关的例子.
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| 关 键 词： | B-稳定理想 正则理想 模消去律 |
On B-Stably Regular Ideals of a Ring |
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| CHEN Huanyin.On B-Stably Regular Ideals of a Ring[J].Chinese Annals of Mathematics,2012,33(1):123-132. |
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| Authors: | CHEN Huanyin |
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| Affiliation: | CHEN Huanyin1 1 Department of Mathematics,Hangzhou Normal University,Hangzhou 310036, China. |
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| Abstract: | In this paper,the author investigates the necessary and sufficient conditions under which a regular ideal is B-stable.It is shown that a regular ideal I of a ring R is B-stable if and only if for any finitely generated projective right R-module A,if A1 and A2 are finitely generated submodules of A such that A1≌A2,A1= A1I and A2 = A2I,there exists a finitely generated submodule B of A,such that A = A1 ? B = A2 ? B;if and only if for any idempotents e,f∈I,eR≌fR implies eR/（eR∩fR） = fR/（eR∩fR）;if and only if for any a∈1 + I,there exists an idempotent e∈I,such that a- e∈U（R） and aR∩eR= 0.Related examples are constructed as well. |
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| Keywords: | B-Stable ideal Regular ideal Cancellation of module |
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