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A NOTE ON GRADED RING WITH PRIME SPECTRUM
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In this paper, we study some algebraic and topological properties of the complement Zariski topology of a graded ideal in a commutative ring. We also determine both algebraic and topological characterizations.
Abstract
In this paper, we study some algebraic and topological properties of the complement Zariski topology of a graded ideal in a commutative ring. We also determine both algebraic and topological characterizations.
참고문헌 (13)
- M.F. Atiyah, "Introduction to Commutative Algebra" (1969), Addison-Wesley
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- N. Bourbaki, "Elements of Mathematics General Topology Part 1 and Part 2" (1966), Hermann and Addison-Wesley
- A. Y. Darani, "Topologies on <TEX>$Spec_g(M)$<", TEX>, 2011, pp.3, 45~53
- C.P. Lu, "The Zariski Topology on The Prime Spectrum of a Module", Houston J. Math., 25, pp.417~432 (1999)
- C.P. Lu, "Modules with Noetherian Spectrum", Comm. in Algebra, 38, pp.807~828 (2010)[DOI]
- R. L. McCasland, "On the Spectrum of a Module over a Commutative Ring", Comm. in Algebra, 25, pp.79~103 (1997)[DOI]
- C. Nastasescu, "Graded Ring Theory" (1982), North Holand
- M. Refai, "On Graded Primary Ideals", Turkish J. Mathematics, 28, pp.217~229 (2004)
- P.C. Roberts, "Multiplicities and Chern classes in local algebra" (1998), Cambridge University Press
- M. Alkan, "Zariski Subspace Topologies Associated with Ideals", 30th International Conference of the Jangjeon Mathematical Society (ICJMS 20l7), pp.155~157 (2017)
- O. Zariski, "Commutative Algebra Vol. 1" (1975), Springer-Verlag
관련 논문AI추천
The homogeneous spectrum of a graded commutative ring by torsion groupMohamed Aqalmoun, Yassir Mata대한수학회 · 대한수학회보2025 · 제62권 제1호On Graded Quasi-Prime SubmodulesKhaldoun Al-Zoubi, Rashid Abu-Dawwas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제2호ON DUAL ZARISKI TOPOLOGY OVER GRADED COMULTIPLICATION MODULESAzzh Saad Alshehry, Rashid Abu-Dawwas대한수학회 · 대한수학회논문집2021 · 제36권 제1호On graded $N$-irreducible ideals of commutative graded ringsAnass Assarrar, Najib Mahdou대한수학회 · 대한수학회논문집2023 · 제38권 제4호On graded $J$-ideals over graded ringsEce Yetkin Celikel, Malik Bataineh, Tamem Al-Shorman대한수학회 · 대한수학회논문집2023 · 제38권 제2호Topological dimension of pseudo-prime spectrum of modulesDawood Hassanzadeh-Lelekaami, Hajar Roshan-Shekalgourabi대한수학회 · 대한수학회논문집2017 · 제32권 제3호
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