1. Introduction. In ring theory, it is well known that regular rings without non-zero nilpotent
elements are characterized in terms of quasi-ideals, that is, the following conditions on a ring …

In this paper, we consider the N-pure notion. An ideal $ I $ of a ring $ R $ is said to be N-
pure, if for every $ a\in I $ there exists $ b\in I $ such that $ a (1-b)\in N (R) $, where N (R) is …

A non-empty subset U of a near-ring N is said to be a semigroup left (resp. right) ideal of N if
NU⊆ U (resp. UN⊆ U) and if U is both a semigroup left ideal and a semigroup right ideal, it …

In near-ring theory several different types of primitivity exist. These all imply several different
types of primeness. In case of near-rings with DCCN most of the types of primeness are …

In this paper the terms, regular near-rings, r-regular near-rings, symmetric near-ring, weakly
regular near-ring, completely prime ideal, 1-prime ideal, 1-semiprime ideals are introduced …

On Almost Primary Ideals 1 Introduction Page 1 International Journal of Algebra, Vol. 5, 2011,
no. 13, 627 - 636 On Almost Primary Ideals Adil Kadir Jabbar and Chwas Abas Ahmed …

A U-ring is a ring in which every subring is a meta ideal. A meta ideal of a ring R is a subring
I of R which lies in a chain of subrings, with the properties:(1) Iλ is an ideal of Iλ+ 1 for all λ< …

Almost prime ideal in gamma near ring Page 1 EUROPEAN JOURNAL OF PURE AND APPLIED
MATHEMATICS Vol. 11, No. 2, 2018, 449-456 ISSN 1307-5543 – www.ejpam.com Published …

We show that a finite minimal left ideal L of a zero symmetric near-ring N is a planar near-
ring if L is not contained in the radical J 2 (N). This result will follow from a more general …

Let $ R $ be a commutative ring. The purpose of this article is to introduce a new class of
ideals of R called weakly irreducible ideals. This class could be a generalization of the …