[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c160230

TOPOLOGICAL DIMENSION OF PSEUDO-PRIME SPECTRUM OF MODULES

Hassanzadeh-Lelekaami, Dawood (Department of Basic Sciences Arak University of Technology)
Roshan-Shekalgourabi, Hajar (Department of Basic Sciences Arak University of Technology)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.3, 2017 , pp. 553-563 More about this Journal

Abstract

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

Keywords

pseudo-prime submodule; Zariski topology; topological module; Noetherian space; combinatorial dimension;

Citations & Related Records

Reference

1	D. Hassanzadeh-Lelekaami and H. Roshan-Shekalgourabi, Pseudo-prime submodules of modules, Math. Rep. (Bucur.) 18(68) (2016), no. 4, 591-608.
2	I. Kaplansky, Commutative rings, University of Chicago Press, 1974.
3	C.-P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math. 33 (2007), no. 1, 125-143.
4	H.Matsumura, Commutative ring theory, Cambridge: Campridge University, Press, 1986.
5	J. Ohm and R. L. Pendleton, Rings with Noetherian spectrum, Duke Math. J. 35 (1968), 631-640. DOI
6	Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra 16 (1988), no. 4, 755-779. DOI
7	A. Barnard, Multiplication modules, J. Algebra 71 (1981), no. 1, 174-178. DOI
8	N. Bourbaki, Elements of Mathematics. Commutative Algebra, Addison-Wesley, Publishing Co., 1972.
9	M. P. Brodmann and R. Y. Sharp, Local Cohomology an Algebraic Introduction with Geometric Applications, Cambridge Univercity Press, 1998.