关于v-Noether环

On v-Noetherian Rings

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.