Commutative Algebra and Its Applications

Let R be a commutative ring with $1{\neq}0$ . In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$ , then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sq…

• ECE YETKİN ÇELİKEL

Let R be a commutative ring with $1{\neq}0$ . In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$ , then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sq…

• ATIF BAYRAMOĞLU
• ÜNSAL TEKİR

Let R be a commutative ring with $1{\neq}0$ . In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever $a,b,c{\in}R$ and $abc{\in}I$ , then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sq…

• ECE YETKİN ÇELİKEL

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for all 1 ≤ i ≤ n.Let be a finite direct sum of R-modules Mi . We prove that M is (quasi-) discrete if and only if are relative…

• DERYA KESKİN TÜTÜNCÜ

Let R be a ring and M a right R-module. The module M is a CS-module or satifies (C1) if every submodule is essential in a direct summand of M. In this note we investigate two generalizations of CS-modules.

• ADNAN TERCAN

No abstract yet.

• AYESHA ASLOOB TOPAÇOĞLU

Abstract A module M is called poor whenever it is N-injective, then the module N is semisimple. In this paper the properties of poor modules are investigated and are used to characterize various families of rings.

• MUSTAFA ALKAN

Let [Formula: see text] be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1-absorbing primary ideals in commutative rings. A proper ideal [Formula: see text] of [Formula: see text] is called a [Formula: see text]-absorbing primary ideal of [Formula: see text] if whenever nonunit e…

• ECE YETKİN ÇELİKEL

No abstract yet.

• AYESHA ASLOOB TOPAÇOĞLU

No abstract yet.

• EMRE COŞKUN

No abstract yet.

In this article, we define a module M to be 𝒢-extending if and only if for each X ≤ M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We consider the decomposition theory for 𝒢-extending modules and give a characterization of the Abelian groups which are 𝒢-extending. In contrast to t…

• ADNAN TERCAN
• EVRİM AKALAN