منابع مشابه
A Note on א0-injective Rings
A ring R is called right א0-injective if every right homomorphism from a countably generated right ideal of R to RR can be extended to a homomorphism from RR to RR. In this note, some characterizations of א0-injective rings are given. It is proved that if R is semiperfect, then R is right א0injective if and only if every homomorphism from a countably generated small right ideal of R to RR can b...
متن کاملOn semiperfect rings of injective dimension one
We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.
متن کاملRepresentation of algebraic distributive lattices with א 1 compact elements as ideal lattices of regular rings
We prove the following result: Theorem. Every algebraic distributive lattice D with at most א1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the א1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. F...
متن کاملCommuting $pi$-regular rings
R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.
متن کاملOn Regular Group Rings
Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1986
ISSN: 0022-4049
DOI: 10.1016/0022-4049(86)90073-3