In this paper, we generalize the concepts of prime and primary ideals in terms of ɸ-prime
and ɸ-primary ideals in a commutative semiring S with non-zero identity. We also introduce …

In [1] Nicholson and Zhou named a ring ܦ clean if all elements a in ܦ can be written as a
sum of a unit and an idempotent. This paper is a continuation of stud rings relative to nil …

Abstract Marks (J. Algebra 280 (2004) 463–471) proved that if the skew polynomial ring R x;
σ R x; σ is left or right duo, then R x; σ R x; σ is commutative. It is proved that if R x; σ R x; σ is …

In this paper, we introduce the new concept of nonnil-commutative diagrams (resp., nonnil-
projective modules) as a generalization of commutative diagrams (resp., projective …

This paper examines the radical formula in noncommutative case and for this purpose, a
generalization of prime submodule is defined. It is proved that there is a direct connection …

In this note we are concerned with relationships between one-sided ideals and two-sided
ideals, and study the properties of polynomial rings whose maximal one-sided ideals are …

A near-ring N is called weak commutative (Definition 9.4, p. 289, Pilz [7]) if xyz= xzy for every
x, y, z∈ N. It is quite natural to investigate the properties of N if xyz= zyx for every x, y, z∈ N …

In this paper, we introduce the concept of Σ-semicommutative ring for Σ a finite family of
endomorphisms of a ring R. We relate this class of rings with other classes of rings such as …

Let R be a commutative ring with 1 and M be an unitary R-module. Prime and semiprime
submodules of M are defined as follows. An R-submodule P of M is called a prime …