On (m, n)-semiprime submodules

Pekin A., Koç S., Ugurlu E. A.

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, vol.70, no.3, pp.260-267, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3176/proc.2021.3.05
  • Journal Name: PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Agricultural & Environmental Science Database, Aquatic Science & Fisheries Abstracts (ASFA), Biotechnology Research Abstracts, Central & Eastern European Academic Source (CEEAS), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.260-267
  • Keywords: semiprime submodule, (m,n)-closed ideal, (m,n)-semiprime submodule, von Neumann regular module, descending chain condition

Abstract

This paper aims to introduce a new class of submodules, called (m, n)-semiprime submodule, which is a generalization of semiprime submodule. Let M be a unital A-module and m,n is an element of N. Then a proper submodule P of M is said to be an (m, n)-semiprime submodule if whenever a(m)x is an element of P for some a is an element of A,x is an element of M, then a(n)x is an element of P. In addition to giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules.