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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)

  1. M.F. Atiyah, "Introduction to Commutative Algebra" (1969), Addison-Wesley
  2. E. Kunz, "Introduction to Commutative Algebra and Algebraic Geometry" (1985), Birkhauser
  3. D.G. Northcott, "Lessons on Rings, Modules and Multiplicities" (1968), Cambridge University Press
  4. N. Bourbaki, "Elements of Mathematics General Topology Part 1 and Part 2" (1966), Hermann and Addison-Wesley
  5. A. Y. Darani, "Topologies on <TEX>$Spec_g(M)$<", TEX>, 2011, pp.3, 45~53
  6. C.P. Lu, "The Zariski Topology on The Prime Spectrum of a Module", Houston J. Math., 25, pp.417~432 (1999)
  7. C.P. Lu, "Modules with Noetherian Spectrum", Comm. in Algebra, 38, pp.807~828 (2010)[DOI]
  8. R. L. McCasland, "On the Spectrum of a Module over a Commutative Ring", Comm. in Algebra, 25, pp.79~103 (1997)[DOI]
  9. C. Nastasescu, "Graded Ring Theory" (1982), North Holand
  10. M. Refai, "On Graded Primary Ideals", Turkish J. Mathematics, 28, pp.217~229 (2004)
  11. P.C. Roberts, "Multiplicities and Chern classes in local algebra" (1998), Cambridge University Press
  12. M. Alkan, "Zariski Subspace Topologies Associated with Ideals", 30th International Conference of the Jangjeon Mathematical Society (ICJMS 20l7), pp.155~157 (2017)
  13. O. Zariski, "Commutative Algebra Vol. 1" (1975), Springer-Verlag

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