This paper is devoted to introducing and studying two concepts, σ-skew strongly M-reflexive
and σ-skew strongly M-nil-reflexive on monoid rings, which are generalizations of strongly M …

Characterizations of Morita context rings satisfying various additional ring properties,
including reflexive, semiprime, prime, NI, weakly 2-primal and 2-primal, are given. The …

The classes of semicommutative, PS I, 2-primal, weakly-2-primal, NI, NR and Dedekind-finite
rings form a strictly increasing chain of classes of rings. Examples have been provided by …

Lambek extended the usual commutative ideal theory to ideals in noncommutative rings,
calling an ideal A of a ring R symmetric if rst∈ A implies rts∈ A for r, s, t∈ R. R is usually …

The reversible property of rings was initially introduced by Habeb and plays a role in
noncommutative ring theory. In this note we study the reversible ring property on nilpotent …

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new
approach to reflexive property for rings by using nilpotent elements, in this direction we …

The reflexive property for ideals was introduced by Mason and has important roles in
noncommutative ring theory. In this note we study the structure of idempotents satisfying the …

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new
approaches to reflexive property for rings by using nilpotent elements. In this direction we …

The RIP of rings was introduced by Kwak and Lee as a generalization of the one-sided
idempotent-reflexivity property. In this study, we focus on rings in which all one-sided …

It has recently been shown that a minimal reversible nonsymmetric ring has order 256
answering a question originally posed in a paper on a taxonomy of 2-primal rings. In a …