| 关于v-Noether环 |
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| 引用本文： | 田艳,王芳贵. 关于v-Noether环[J]. 四川师范大学学报(自然科学版), 2010, 33(3). DOI: 10.3969/j.issn.1001-8395.2010.03.004 |
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| 作者姓名： | 田艳 王芳贵 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 国家自然科学基金，教育部博士点专项科研基金 |
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| 摘 要： | Mori整环是v-理想满足升链条件的整环,将其研究扩大到有零因子的交换环上.v-Noether环被定义为v-理想满足升链条件的交换环.若R是v-Noether环,P是素理想,则R[P]是v-Noether环.而且还得到:若R中每个非零理想都被包含在至多有限个极大t-理想中,R是v-Noether环当且仅当对于每个极大t-理想M而言,R[M]都是v-Noether环.
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| 关 键 词： | v-理想 t-理想 v-Noether环 |
On v-Noetherian Rings |
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| TIAN Yan,WANG Fang-gui. On v-Noetherian Rings[J]. Journal of Sichuan Normal University(Natural Science), 2010, 33(3). DOI: 10.3969/j.issn.1001-8395.2010.03.004 |
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| Authors: | TIAN Yan WANG Fang-gui |
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| Affiliation: | TIAN Yan,WANG Fang-gui(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan) |
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| Abstract: | A Mori domain is an integral domain which satisfies the ascending chain condition on v-ideals.In this paper the study is extended to commutative rings with zero divisors.A v-Noetherian ring is defined to be a ring which satisfies the ascending chain condition on v-ideals.We prove that if R is a v-Noetherian ring and P is a prime ideal,then R[P] is a v-Noetherian ring.Moreover we also show that if each nonzero ideal is contained in at most finitely many maximal t-ideals,then R is a v-Noetherian ring if and o... |
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| Keywords: | v-ideal t-ideal v-Noetherian rings |
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