Countably McCoy rings

On Semiprime Right Goldie Mccoy Rings

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

on weak mccoy rings

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

Countably Generated Ideals in Rings of Continuous Functions

1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...

Countably Thick Modules

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes M of modules in σ[M ] we study when direct sums of modules from M satisfies a property P in σ[M ]. In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

Countably Convex Gæ Sets