Ginn and Moss proved that a two sided Noetherian ring with essential right socle is right and
left Artinian. We prove that is a right Artinian ring whose the Jacobson radical is equivalent to …

In this paper we prove that a right Noetherian ring (with identity) in which each right ideal is a
right annihilator must be right Artinian, and we then use this result to give a characterization …

A result of Ginn and Moss asserts that a left and right noetherian ring with essential right
socle is left and right artinian. There are examples of right finitely embedded rings with ACC …

In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if
and only if (i) for any nonzero right module, there is a nonzero linear map from it to a …

A Characterization of Right Artinian Rings KYUNGPOOK MATHEMATICAL JOURNAL
OPEN ACCESS eISSN 0454-8124 pISSN 1225-6951 QR Code KYUNGPOOK …

Let R be a ring with second singular right ideal and second singular left ideal. Motivated by a
result in Zhou (Zhou, Y.(2002). Rings in which certain right ideals are direct summands of …

This note contains the following results for a ring A:(1) A is a quasi-Frobenius ring iff A is a
left and right YJ-injective, left Noetherian ring whose prime factor rings are right YJ-injective …

Let R be a ring. An R-module M is finitely annihilated if the annihilator of M is the annihilator
of a finite subset of M. It is proved that if R has right socle S then the ring R/S is right Artinian …

It is shown that if R is a right automorphism-invariant ring and satisfies ACC on right
annihilators, then R is a semiprimary ring. By this useful fact, we study finiteness conditions …

Left д-injective ringsИ which extend left self injective ringsИ have been considered in
several papers (cf. for exampleИ [10]-[14]). The following generalizations of left д-injective …