Describing the subgroup structure of a non-commutative division ring is subject an intensive study in theory rings particular, and skew linear groups general. This still so far to be complete. In present paper, we this problem for weakly locally finite rings. Such constitute large class which strictly contains

Additive cyclic codes over Galois rings were investigated in [3]. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in [3], whereas the other one has some unusual propertie...

We give an exposition and generalization of Orlov’s theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary non-commutative right noetherian ring of finite global dimension. A short treatment of some foundations for local cohomology and Grothendieck duality at this ...

it is shown that a commutative reduced ring r is a baer ring if and only if it is a cs-ring; if and only if every dense subset of spec (r) containing max (r) is an extremally disconnected space; if and only if every non-zero ideal of r is essential in a principal ideal generated by an idempotent.

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).

It is proved for certain graded non-commutative rings that if M and N are graded bi-modules, finitely generated from either side, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. Among the rings in question are twisted homogeneous coordinate rings of elliptic curves.

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.