关于v-Noether环  

On v-Noetherian Rings

作　　者：田艳[1] 王芳贵[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2010年第3期295-297,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10671137);教育部博士点专项科研基金(20060636001)资助项目

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.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 only if for each maximal t-ideal M,R[M] is a v-Noetherian ring.

关 键 词：v-理想 t-理想 v-Noether环 

分 类 号：O154[理学—数学]