Z. Bilgin, S. Koç, A. Özkirişci, “Strongly prime submodules and strongly 0-dimensional modules”, Algebra Discrete Math., 2019, Volume 28, Issue 2,Pages <nobr>171

RESEARCH ARTICLE

Strongly prime submodules and strongly 0-dimensional modules

Z. Bilgin^a, S. Koç^b, A. Özkirişci^c

^a Philosophy Department, Istanbul Medeniyet University 34000, Kadikoy, Istanbul, Turkey
^b Department of Mathematics, Faculty of Science and Arts, Marmara University 34722, Istanbul, Turkey
^c Department of Mathematics, Faculty of Science and Arts, Yildiz Technical University 34210, Istanbul, Turkey

Abstract: In this work, we study strongly prime submodules and strongly 0-dimensional modules. We give some equivalent conditions for being a strongly 0-dimensional module. Besides we show that the quasi-Zariski topology on the spectrum of a strongly 0-dimensional module satisfies all separation axioms and it is a metrizable space.

Keywords: strongly prime submodule, strongly 0-dimensional module, multiplication module, quasi-Zariski topology.

MSC: Primary 13A15, 13A99, 13C05, 13C99; Secondary 13E15, 13E99

Received: 29.03.2018
Revised: 18.09.2018

Language: English