Some results on N-pure ideals (original) (raw)
Related papers
arXiv: Commutative Algebra, 2020
In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it mid ring. Also, we provide new characterizations for von Neumann regular and zero-dimensional rings. Moreover, some results about mp-ring are given. Finally, a characterization for mid rings is provided. Then it is shown that the class of mid rings is strictly between the class of reduced mp-rings (p.f. rings) and the class of mp-rings.
2012
In this paper, we introduced the notion of N-ideals on rings and investigated some related properties
On Rings whose Maximal Essential Ideals are Pure
AL-Rafidain Journal of Computer Sciences and Mathematics, 2007
This paper introduces the notion of a right MEP-ring (a ring in which every maximal essential right ideal is left pure) with some of their basic properties; we also give necessary and sufficient conditions for MEPrings to be strongly regular rings and weakly regular rings.
Maximal Generalization of Pure Ideals
2008
The purpose of this paper is to study the class of the rings for which every maximal right ideal is left GP-ideal. Such rings are called MGP-rings and give some of their basic properties as well as the relation between MGP-rings, strongly regular ring, weakly regular ring and kasch ring.
On ideals with the Rees property
Archiv der Mathematik, 2013
A homogeneous ideal I of a polynomial ring S is said to have the Rees property if, for any homogeneous ideal J ⊂ S which contains I, the number of generators of J is smaller than or equal to that of I. A homogeneous ideal I ⊂ S is said to be m-full if mI : y = I for some y ∈ m, where m is the graded maximal ideal of S. It was proved by one of the authors that m-full ideals have the Rees property and that the converse holds in a polynomial ring with two variables. In this note, we give examples of ideals which have the Rees property but are not m-full in a polynomial ring with more than two variables. To prove this result, we also show that every Artinian monomial almost complete intersection in three variables has the Sperner property.
2008
In this paper we introduce the notion of "strong nnn-perfect rings" which is in some way a generalization of the notion of "$n$-perfect rings". We are mainly concerned with those class of rings in the context of pullbacks. Also we exhibit a class of nnn-perfect rings that are not strong nnn-perfect rings. Finally, we establish the transfer of this notion
ON STRONG n-PERFECT AND (n, d)-PERFECT RINGS
we study the transfer of the strong n-perfect property and the (n, d)-perfect property from a commutative ring to its subring retract. And we give necessary and sufficient conditions so that some trivial ring extensions be (n, d)-perfect (resp., strong n-perfect) ring. Our results generate new families of examples of rings with zero-divisors satisfying these properties.
On some characterizations of regular and potent rings relative to right ideals
Novi Sad Journal of Mathematics, 2018
In this paper we study the notion of regular rings relative to right ideals, and we give another characterization of these rings. Also, we introduce the concept of an annihilator relative to a right ideal. Basic properties of this concept are proved. New results obtained include necessary and sufficient conditions for a ring to be regular (potent) relative to right ideal.