direct product of rings

In section six, we investigate the Gorcnstcin injective dimensions in direct products of rings, the main result is the following:Let R =ΠR_i be a direct product of rings and let M = M_1 (?)M_2(?)……(?)M_n be adecomposition of an R-module into R_i modules.

第六节研究了环的直积上的Gorenstein内射维数,得到下面结论:设R=ΠR_i(i=1,2。

The least skew-ring congruence on E-inversive E-semiring is described,and the structure of a class of E-inversive E-semiring is obtained,which is the subdirect product of distributive lattice and skew-ring.

首先引入和描述了E-逆E半环上的最小拟环同余,然后刻画了是分配格和拟环的次直积的E-逆E半环。

In this paper, the fuzzy uniform ring, fuzzy uniform subring, fuzzy uniform residue class ring, and direct product of fuzzy uniform rings are defined; the three necessary and sufficient conditions to describe fuzzy uniform ring by the fuzzy topological ring of type (QU), by fuzzy uniform space and by a family of fuzzy subsets of a ring are obtained.

本文定义了模糊一致环概念,研究了它与模糊拓扑环的关系及它与模糊一致空间的关系;给出了借助于环的模糊子集族对模糊一致环的刻画,还引入了模糊一致子环,模糊一致剩余类环与模糊一致环的直积;并讨论了它们的分离性。

In this paper,two products of fuzzy topological rings and of fuzzy topological of type (QU) are defined to prove that the product of fuzzy topological rings is also a fuzzy topological rings.

本文定义了模糊拓扑环的直积 ,论证了该定义的合理性 ;证明了 (QU)型模糊拓扑环的直积仍是 (QU)型模糊拓扑环 ;并研究了 (QU)型模糊拓扑环直积的性质 。