On (<i>m, n</i>)-semiprime submodules

PEKİN A., KOÇ S., Ugurlu E. A.

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, cilt.70, sa.3, ss.260-267, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3176/proc.2021.3.05
  • Dergi Adı: PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-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
  • Sayfa Sayıları: ss.260-267
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.