Now showing items 1-15 of 15

• #### 1-absorbing primary submodules ﻿

(OVIDIUS UNIV PRESS, 2021)
Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is ...
• #### A new generalızatıon of (m, n)-closed ıdeals ﻿

Let R be a commutative ring with identity. For positive integers m and n, Anderson and Badawi (Journal of Algebra and Its Applications 16(1):1750013 (21 pp), 2017) defined an ideal I of a ring R to be an (m,n)-closed if ...

(KOREAN MATHEMATICAL SOC, 2023)
• #### On nonnil-S-Noetherian and nonnil-u-S-Noetherian rings ﻿

Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Then R is called a nonnil-S-Noetherian ring if every nonnil ideal of R is S-finite. Also, R is called a u-S-Noetherian ring if there ...
• #### On S-2-Prime Ideals Of Commutative Rings ﻿

Prime ideals and their generalizations are crucial in numerous research areas, particularly in commutative algebra. The concept of generalization of prime ideals begins with the study of weakly prime ideals. Since then, ...
• #### On s-clean and s-nıl-clean rıngs ﻿

(Jangjeon Research Institute for Mathematical Sciences and Physics, 2024)
Let A be a commutative ring with identity. An element a G A is said to be S-clean (resp., S-nil-clean), where S ⊂ A is a given multiplicative set, if there exists s ∈ S such that sa is clean (resp.. nil-clean). The ring A ...
• #### On weakly 1-Absorbing primary ıdeals of commutative rings ﻿

(WORLD SCIENTIFIC PUBL CO PTE LTD, JUN 2022)
Let R be a commutative ring with 1 not equal 0. We introduce the concept of weakly 1-absorbing primary ideal, which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is said to be weakly 1-absorbing ...
• #### On weakly S-primary ideals of commutative rings ﻿

(WORLD SCIENTIFIC PUBL CO PTE LTD, APR 2023)
Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. ...
• #### On weakly S-primary submodules ﻿

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :R M) n S = 0 to be weakly S-primary if there ...
• #### Prime ideal sum graph of a commutative ring ﻿

(World Scıentıfıc Publ Co Pte Ltd, JUN 2023)
Let R be a commutative ring with identity. The prime ideal sum graph of R, denoted by PIS(R), is a graph whose vertices are nonzero proper ideals of R and two distinct vertices I and J are adjacent if and only if I J is a ...
• #### Quasi J-ideals of commutative rings ﻿

(SPRINGER-VERLAG ITALIA SRL, JUN 2022)
Let R be a commutative ring with identity. In this paper, we introduce the concept of quasi J-ideal which is a generalization of J-ideal. A proper ideal of R is called a quasi J-ideal if its radical is a J-ideal. Many ...
• #### Quasi-S-primary ideals of commutative rings ﻿

(TAYLOR & FRANCIS INC, OCT 3 2023)
Let R be a commutative ring with 1 not equal 0 and S be a multiplicatively closed subset of R. We call an ideal I of R disjoint with S quasi-S-primary if there exists an s is an element of S such that whenever a, b is an ...
• #### Semi r-ideals of commutative rings ﻿

(OVIDIUS UNIV PRESS, MAR 1 2023)
For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi ...
• #### Weakly J-Ideals of Commutative Rings ﻿

Let R be a commutative ring with non-zero identity.In this paper, we introduce the concept of weakly J-ideals as a new generalization of J-ideals. We call a proper ideal I of a ring R a weakly J-ideal if whenever a, b is ...
• #### Weakly J-submodules of modules over commutative rings ﻿

(WORLD SCIENTIFIC PUBL CO PTE LTD, JUL 2023)
Let R be a commutative ring with identity and M be a unitary R-module. By J(R), we denote the Jacobson radical of R. The purpose of this paper is to introduce the concept of weakly J-submodules generalizing J-submodules. ...