Right primary and nilary rings and ideals

GF Birkenmeier, JY Kim, JK Park - Journal of Algebra, 2013 - Elsevier
Recall that in a commutative ring R an ideal I is called primary if whenever a, b∈ R with
ab∈ I then either a∈ I or bn∈ I, for some positive integer n. A commutative ring R is called …

Extension of almost primary ideals to noncommutative rings and the generalization of nilary ideals

A Abouhalaka, Ş Fındık - Mathematics, 2023 - mdpi.com
In this paper, we introduce the concepts of almost right primary ideals and almost nilary
ideals and study their related results. We compare almost right primary ideals with other …

A generalization of symmetric ring property

HK Kim, TK Kwak, SI Lee, Y Lee, SJ Yun - 대한수학회보, 2016 - dbpia.co.kr
{This note focuses on a ring property in which upper and lower nilradicals coincide, as a
generalizations of symmetric rings. The concept of symmetric ideal and ring in the …

On left O-prime ideals over a noncommutative ring

O ÖNE, M ALKAN - Advanced Studies in Contemporary Mathematics, 2017 - dbpia.co.kr
In this paper, we focus on a one-sided generalization of the concept of prime ideal in a
noncommutative ring, which is called a left O-prime ideal. Some of its basic properties are …

Rings with prime nilradical

A Badawi, TG Lucas - Arithmetical properties of commutative rings …, 2005 - taylorfrancis.com
A commutative ring R is said to be a φ-ring if its nilradical Nil (R) is both prime and divided,
the latter meaning Nil (R) is comparable with each principal ideal of R. Special types include …

[PDF][PDF] δ-primary ideals of commutative rings

Z Dongsheng - Kyungpook Math. J, 2001 - researchgate.net
In this paper we investigate δ-primary ideals which unify prime ideals and primary ideals. A
number of main results about prime ideals and primary ideals are extended into this general …

On rings with nil commutator ideal

H Abu-Khuzam - Bulletin of the Australian Mathematical Society, 1981 - cambridge.org
On rings with nil commutator ideal Page 1 BULL. AUSTRAL. MATH. SOC. I6A70 VOL. 23 (1981),
307-311. ON RINGS WITH NIL COMMUTATOR IDEAL HAZAR ABU-KHUZAM Let R be a ring …

Rings over which every semi-primary ideal is 1-absorbing primary

FAA Almahdi, M Tamekkante… - Communications in …, 2020 - Taylor & Francis
Let R be commutative ring with 1≠ 0. A proper ideal I of R is called a 1-absorbing primary
ideal of R if whenever nonunit elements a, b, c∈ R and abc∈ I, then ab∈ I or c∈ I. It is …

Commutative rings whose proper ideals are serial

M Behboodi, S Heidari - Algebras and Representation Theory, 2017 - Springer
A result of Nakayama and Skornyakov states that a ring R is an Artinian serial ring if and
only if every R-module is serial. This motivated us to study commutative rings for which every …

[图书][B] Generalized primary rings

CE Gorton - 2006 - search.proquest.com
The concept of a primary ideal in commutative rings has been extended in several ways to
noncommutative ring theory. Generically these are called generalized primary conditions …