Ajim Uddin Ansari - Academia.edu (original) (raw)
I am an Assistant Professor in Mathematics at the CMP Degree College, University of Allahabad, Prayagraj (UP), India.
Supervisors: Dr B. K. Sharma and Prof. Shiv Datt Kumar
Address: Department of Mathematics, CMP Degree College, University of Allahabad, Prayagraj, India
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Papers by Ajim Uddin Ansari
arXiv (Cornell University), Dec 31, 2023
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Communications in algebra, May 15, 2024
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Iranian Journal of Mathematical Sciences and Informatics, Sep 1, 2022
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International Electronic Journal of Algebra, 2020
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International Electronic Journal of Algebra
Let GGG be an abelian group and SSS a given multiplicatively closed subset of a commutative GGG-g... more Let GGG be an abelian group and SSS a given multiplicatively closed subset of a commutative GGG-graded ring AAA consisting of homogeneous elements. In this paper, we introduce and study GGG-graded SSS-Noetherian modules which are a generalization of SSS-Noetherian modules. We characterize GGG-graded SSS-Noetherian modules in terms of SSS-Noetherian modules. For instance, a GGG-graded AAA-module MMM is GGG-graded SSS-Noetherian if and only if MMM is SSS-Noetherian, provided GGG is finitely generated and SSS is countable. Also, we generalize some results on GGG-graded Noetherian rings and modules to GGG-graded SSS-Noetherian rings and modules.
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International Electronic Journal of Algebra, 2020
In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer doma... more In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer domain to the graded case. We generalize several types of prime ideals associated to a module over a ring to the graded case and prove that most of them coincide over a graded Prüfer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prüfer domain under certain conditions and give some applications of it.
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International Electronic Journal of Algebra, 2020
In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer doma... more In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer domain to the graded case. We generalize several types of prime ideals associated to a module over a ring to the graded case and prove that most of them coincide over a graded Prüfer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prüfer domain under certain conditions and give some applications of it.
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arXiv (Cornell University), Dec 31, 2023
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Communications in algebra, May 15, 2024
Bookmarks Related papers MentionsView impact
Iranian Journal of Mathematical Sciences and Informatics, Sep 1, 2022
Bookmarks Related papers MentionsView impact
International Electronic Journal of Algebra, 2020
Bookmarks Related papers MentionsView impact
International Electronic Journal of Algebra
Let GGG be an abelian group and SSS a given multiplicatively closed subset of a commutative GGG-g... more Let GGG be an abelian group and SSS a given multiplicatively closed subset of a commutative GGG-graded ring AAA consisting of homogeneous elements. In this paper, we introduce and study GGG-graded SSS-Noetherian modules which are a generalization of SSS-Noetherian modules. We characterize GGG-graded SSS-Noetherian modules in terms of SSS-Noetherian modules. For instance, a GGG-graded AAA-module MMM is GGG-graded SSS-Noetherian if and only if MMM is SSS-Noetherian, provided GGG is finitely generated and SSS is countable. Also, we generalize some results on GGG-graded Noetherian rings and modules to GGG-graded SSS-Noetherian rings and modules.
Bookmarks Related papers MentionsView impact
International Electronic Journal of Algebra, 2020
In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer doma... more In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer domain to the graded case. We generalize several types of prime ideals associated to a module over a ring to the graded case and prove that most of them coincide over a graded Prüfer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prüfer domain under certain conditions and give some applications of it.
Bookmarks Related papers MentionsView impact
International Electronic Journal of Algebra, 2020
In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer doma... more In this paper, we introduce the notion of graded Prüfer domain as a generalization of Prüfer domain to the graded case. We generalize several types of prime ideals associated to a module over a ring to the graded case and prove that most of them coincide over a graded Prüfer domain. Moreover, we investigate the graded primary decomposition of graded ideals in a graded Prüfer domain under certain conditions and give some applications of it.
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