ON THE PRIME SPECTRUM OF A MODULE OVER A COMMUTATIVE NOETHERIAN RING

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 3,  2007, pp.351-366
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.3.351
Title & Authors
ON THE PRIME SPECTRUM OF A MODULE OVER A COMMUTATIVE NOETHERIAN RING
Ansari-Toroghy, H.; Sarmazdeh-Ovlyaee, R.;

Abstract
Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $\small{Supp_{R}}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.
Keywords
prime submodule;Zariski topology;topological dimensions;
Language
English
Cited by
1.
The Zariski Topology-Graph of Modules Over Commutative Rings, Communications in Algebra, 2014, 42, 8, 3283
References
1.
M.F. Atiyah and I. G. Macdonald, Introduction to commutative Algebra (Addison-Wesley, Reading, Mass., 1969).

2.
N. Bourbaki, Algebra, Chap.S, Hermman, Paris, 1955.

3.
M.P. Brodmann and R. Y. Sharp, Local cohomology an algebraic introduction with geometric applications, cambridge univercity press 1995.

4.
T. Duraivel, Topology on spectrum of module, J. Ramanujan Math. Soc. (1) 9 (1994), 25-34.

5.
Chin-Pi Lu, The Zariski topology on the prime spectrum of a module, Houston Journal of Mathematics (3) 25 1999, 417-432.

6.
Chin-Pi Lu, Spectra of modules, Comm. Algebra (10) 23 1995, 3741-3752.

7.
Chin-Pi Lu, A module whose prime spectrum has the surjective naturl map, Houston Journal of Mathematics (1) 33 2007, 125-143.

8.
S. Yassemi, Coassociated primes over a commutative ring, Math. Scand. 80 1997, 175-185.