We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-pr... more We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-primary ideals. We investigate some characterizations and properties of such new generalization. If P is an n-absorbing I-primary ideal of R and √IP=I√P, then √P is a n-absorbing I-primary ideal of R. And if √P is an (n-1)-absorbing ideal of R such that √(I√P) ⊆IP, then P is an n-absorbing I-primary ideal of R.
Zenodo (CERN European Organization for Nuclear Research), 2023
In this paper, we introduce a generalization of topological R-module using β-open sets called irr... more In this paper, we introduce a generalization of topological R-module using β-open sets called irresolute β-topological algebra (group, ring and module). We show that the center of an irresolute β-hausdorff ring is β-closed and if N is Q-submodule of an irresolute β-topological R-module M, then βCl(N) M is also βCl(Q) R-submodule where Q, N are subsets of R, M respectively. Several other properties of them are investigated.
We define a new generalization of −absorbing ideals in commutative rings called −absorbing −prima... more We define a new generalization of −absorbing ideals in commutative rings called −absorbing −primary ideals. We investigate some characterizations and properties of such new generalization. If is an −absorbing −primary ideal of and √ = √ , then √ is a −absorbing −primary ideal of. And if √ is an (− 1) −absorbing ideal of such that � √ ⊆ , then is an −absorbing −primary ideal of .
Abstract- Given a nonempty set and a function , three fuzzy topological spaces are introduced. So... more Abstract- Given a nonempty set and a function , three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
By a localization property we mean a property that preserved under localizing modules at multipli... more By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its localization at multiplicative closed sets and conversely, that means we determine those conditions which make a given property of a module as a localization property, so we give several conditions under which certain types of modules posses localization property.
In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose... more In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.
Given a nonempty set X and a function f : X 6X, three pseudo-metrizable spaces are introduced. So... more Given a nonempty set X and a function f : X 6X, three pseudo-metrizable spaces are introduced. Some properties of these spaces and relations among them are studied and discussed.
In this paper, we study some properties of φ-prime submodules andwe give another charactrization ... more In this paper, we study some properties of φ-prime submodules andwe give another charactrization for it. For given submodules N and K of a moduleM with K ⊆ N, we prove that N is φ-prime submodule if and only if N/Kis φ_K-prime submodule. Finally, we show that any finite sum of φ-prime submodules isφ-prime.
Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of $R$. In this paper, we ... more Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of $R$. In this paper, we study a certain condition, namely $C_{\frak a}$, introduced by Aghapournahr and Melkersson, on the extension of two subcategories of $R$-modules. We extend and generalize some of the main results of Yoshizawa [Y1,Y2]. As an example of extension of subcategories, we study the weakly Laskerian modules and we find some conditions under which the local cohomology modules of a weakly Laskerian module lie in an arbitrary Serre subcategory. Eventually, we investigate the cofiniteness of the local cohomology modules of weakly Laskerian modules.
In this paper, we give a generalization for weakly primary submodules called $I$-primary submodul... more In this paper, we give a generalization for weakly primary submodules called $I$-primary submodule and we study some properties of it. We give some characterizations of $I$-primary submodules. Also we establish the situation of $I$-primary submodules in module localizations and decomposition modules.
Let R = n∈N 0 R n be a Noetherian homogeneous ring with local base ring (R 0 , m 0 ) and let M an... more Let R = n∈N 0 R n be a Noetherian homogeneous ring with local base ring (R 0 , m 0 ) and let M and N be finitely generated graded R−modules. Let i, j ∈ N 0 . In this paper we will study Artinianess of
Let R = n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and let M and N be ... more Let R = n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and let M and N be finitely generated graded R−modules. Let i,j ∈ N0. In this paper we will study Artinianess of Γm0R(H i
Given a nonempty set X and a function f:X →X , three fuzzy topological spaces are introduced. Som... more Given a nonempty set X and a function f:X →X , three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-pr... more We define a new generalization of n-absorbing ideals in commutative rings called n-absorbing I-primary ideals. We investigate some characterizations and properties of such new generalization. If P is an n-absorbing I-primary ideal of R and √IP=I√P, then √P is a n-absorbing I-primary ideal of R. And if √P is an (n-1)-absorbing ideal of R such that √(I√P) ⊆IP, then P is an n-absorbing I-primary ideal of R.
Zenodo (CERN European Organization for Nuclear Research), 2023
In this paper, we introduce a generalization of topological R-module using β-open sets called irr... more In this paper, we introduce a generalization of topological R-module using β-open sets called irresolute β-topological algebra (group, ring and module). We show that the center of an irresolute β-hausdorff ring is β-closed and if N is Q-submodule of an irresolute β-topological R-module M, then βCl(N) M is also βCl(Q) R-submodule where Q, N are subsets of R, M respectively. Several other properties of them are investigated.
We define a new generalization of −absorbing ideals in commutative rings called −absorbing −prima... more We define a new generalization of −absorbing ideals in commutative rings called −absorbing −primary ideals. We investigate some characterizations and properties of such new generalization. If is an −absorbing −primary ideal of and √ = √ , then √ is a −absorbing −primary ideal of. And if √ is an (− 1) −absorbing ideal of such that � √ ⊆ , then is an −absorbing −primary ideal of .
Abstract- Given a nonempty set and a function , three fuzzy topological spaces are introduced. So... more Abstract- Given a nonempty set and a function , three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
By a localization property we mean a property that preserved under localizing modules at multipli... more By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its localization at multiplicative closed sets and conversely, that means we determine those conditions which make a given property of a module as a localization property, so we give several conditions under which certain types of modules posses localization property.
In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose... more In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties. Moreover, we give conditions under which $I$-prime ideals becomes prime or weakly prime and we construct the view of $I$-prime ideal in decomposite rings.
Given a nonempty set X and a function f : X 6X, three pseudo-metrizable spaces are introduced. So... more Given a nonempty set X and a function f : X 6X, three pseudo-metrizable spaces are introduced. Some properties of these spaces and relations among them are studied and discussed.
In this paper, we study some properties of φ-prime submodules andwe give another charactrization ... more In this paper, we study some properties of φ-prime submodules andwe give another charactrization for it. For given submodules N and K of a moduleM with K ⊆ N, we prove that N is φ-prime submodule if and only if N/Kis φ_K-prime submodule. Finally, we show that any finite sum of φ-prime submodules isφ-prime.
Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of $R$. In this paper, we ... more Let $R$ be a commutative noetherian ring and let $\frak a$ be an ideal of $R$. In this paper, we study a certain condition, namely $C_{\frak a}$, introduced by Aghapournahr and Melkersson, on the extension of two subcategories of $R$-modules. We extend and generalize some of the main results of Yoshizawa [Y1,Y2]. As an example of extension of subcategories, we study the weakly Laskerian modules and we find some conditions under which the local cohomology modules of a weakly Laskerian module lie in an arbitrary Serre subcategory. Eventually, we investigate the cofiniteness of the local cohomology modules of weakly Laskerian modules.
In this paper, we give a generalization for weakly primary submodules called $I$-primary submodul... more In this paper, we give a generalization for weakly primary submodules called $I$-primary submodule and we study some properties of it. We give some characterizations of $I$-primary submodules. Also we establish the situation of $I$-primary submodules in module localizations and decomposition modules.
Let R = n∈N 0 R n be a Noetherian homogeneous ring with local base ring (R 0 , m 0 ) and let M an... more Let R = n∈N 0 R n be a Noetherian homogeneous ring with local base ring (R 0 , m 0 ) and let M and N be finitely generated graded R−modules. Let i, j ∈ N 0 . In this paper we will study Artinianess of
Let R = n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and let M and N be ... more Let R = n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and let M and N be finitely generated graded R−modules. Let i,j ∈ N0. In this paper we will study Artinianess of Γm0R(H i
Given a nonempty set X and a function f:X →X , three fuzzy topological spaces are introduced. Som... more Given a nonempty set X and a function f:X →X , three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
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Papers by Ismael Akray