A ring $ R $, possibly with no identity, is called an ${I_0} $-ring if each one-sided ideal not
contained in the Jacobson radical $ J (R) $ contains a nonzero idempotent. If, in addition …

A ring R is a left qp-ring if each of its left ideals is quasi-projective as a left R-module in the
sense of Wu and Jans. The following results giving the structure of left qp-rings are obtained …

A unital left R-module RM is said to have property (S) if every surjective endomorphism of
RM is an automorphism, the ring R is called left (right) S-ring if every left (right) R-module …

We study the structure of idempotents in polynomial rings, power series rings, concentrating
in the case of rings without identity. In the procedure we introduce right Insertion-of …

A ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius),
denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates …

Introduction and Notation. A ring R is called a (von Neumann) regular ring if for each a in R
there exists an x in R such that a= axa. The notion of regularity has been extended to …

We define a generalized right alternative ring to be a nonassociative ring R satisfying the
hypotheses (1)(ab, c, d)+(a, b,[c, d])= a (b, c, d)+(a, c, d) b, and (2)(a, a, a)= 0, for all a, b, c, d …

A right R-module M is non-singular if xI≠ 0 for all non-zero x∈ M and all essential right
ideals I of R. The module M is torsion-free if Tor1R (M, R/Rr)= 0 for all r∈ R. This paper …

Proof. Let M be the largest strongly regular ideal of R. We first show that every nilpotent
element of R= R/M is a homomorphic image of a nilpotent element of R. Let à= a+ M be an …

Let R be a ring with an identity. A ring R will be called a left (right) q*-ring if every R-
homomorphic image of R as a left (right) R-module is quasi-projective, that is, if every cyclic …