Multiplication modules with prime spectrum

The subject of this paper is the Zariski topology on a multiplication module M over a commutative ring R.We find a characterization for the radical submodule radM(0) and also show that there are proper ideals I1; :::; In of Rsuch that radM(0) = radM((I1:::In)M) . Finally, we prove that the spectrum Spec(M) is irreducible if and only if Mis the finite sum of its submodules, whose T -radicals are prime in M.

PDF

___

[1] Ali MM, Smith DJ. Finite and infinite collections of multiplication modules. Contributions to Algebra and Geometry 2001; 42: 557-573.
[2] Alkan M, Tıraş Y. Projective modules and prime submodules. Czechoslovak Mathematical Journal 2006; 56: 601- 611.
[3] Alkan M, Tıraş Y. On invertible and dense submodules. Communications in Algebra 2004; 32; 3911-3919.
[4] Ameri R. Some properties of Zariski topology of multiplication modules. Houston Journal of Mathematics 2010; 36: 337-344.
[5] Atiyah MF, MacDonald IG. Introduction to Commutative Algebra. London, UK: Addison-Wesley, 1969.
[6] Barnard A. Multiplication modules. Journal of Algebra 1981; 71: 174-178.
[7] Bourbaki N. Elements of Mathematics General Topology Part 1 and Part 2. Massachusetts, USA: Hermann and Addison-Wesley, 1966.
[8] El-Bast Z, Smith PF. Multiplication modules. Communications in Algebra 1988; 16: 755-779.
[9] Kunz E. Introduction to Commutative Algebra and Algebraic Geometry. Boston, US: Birkhauser, 1985.
[10] Lu CP. Modules with Noetherian spectrum. Communications in Algebra 2010; 38: 807-828.
[11] McCasland RL, Moore ME, Smith PF. On the spectrum of a module over a commutative ring. Communications in Algebra 1997; 25: 79-103.
[12] Öneş O, Alkan M. Zariski subspace topologies on ideals. Hacettepe Journal of Mathematics and Statistics 2018. doi: 10.15672/HJMS.2018.597
[13] Öneş O, Alkan M. A note on graded ring with prime spectrum. Advanced Studies in Contemporary Mathematics 2018; 28: 625-634.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

Arşiv