Georgian Mathematical Journal 13 (2006), No. 4, 599--606
Copyright Heldermann Verlag 2006
Finitely Generated Modules and Connectivity
Habibollah Ansari-Toroghy
Dept. of Mathematics, Faculty of Science, Guilan University, P. O. Box 1914, Rasht, Iran
ansari@guilan.ac.ir
Reza Ovlyaee-Sarmazdeh
Dept. of Mathematics, Faculty of Science, Guilan University, P. O. Box 1914, Rasht, Iran
ovlyaee@guilan.ac.ir
Let R be a commutative Noetherian ring and let M be a finitely generated R-module. Let X = SpecR(M) be the topological space with Zariski topology. Our main goal in this paper is to describe the connectedness dimension of X in terms of Krull dimension of some quotient of M and prove that c(SpecR(M)) = c(Supp(M)).
Keywords: Prime submodules, Zariski topology, Noetherian topological space, connectivity.
MSC: 13E05
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