Rings, Modules, and Algebras

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

Let $R$ be a ring. An $R$ -module $M$ is called a (weak) duo module provided every (direct summand) submodule of $M$ is fully invariant. It is proved that if $R$ is a commutative domain with field of fractions $K$ then a torsion-free uniform $R$ -module is a duo module if and only if every element $k$ in $K$ such that…

• AYŞE ÇİĞDEM ÖZCAN

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

Özet henüz yok.

Özet henüz yok.

• DERYA KESKİN TÜTÜNCÜ

Özet henüz yok.

Özet henüz yok.

In this study, we introduce the concepts of $S$-prime submodules and\ $S$% -torsion-free modules, which are generalizations of prime submodules and torsion-free modules. Suppose $S\subseteq R\ $is a multiplicatively closed subset of a commutative ring$\ R$, and let $M$ be a unital $R$-module. A submodule $P\ $of $M\ $…

• TARIK ARABACI

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

Let K be a commutative ring with unity, R a non-commutative prime K-algebra with center Z(R), U the Utumi quotient ring of R, C=Z(U) the extended centroid of R, I a non-zero two-sided ideal of R, H and G non-zero generalized derivations of R. Suppose that f(x1,…,xn) is a non-central multilinear polynomial over K such…

• NURCAN ARGAÇ