On (m,n)-semiprime submodules

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Pekin A., Koç S., Aslankarayiğit Uğurlu E.

Proceedings Of The Estonian Academy Of Sciences, cilt.70, sa.3, ss.1-8, 2021 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 70 Sayı: 3
• Basım Tarihi: 2021
• 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.1-8
• Marmara 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 $m,n\in \mathbb{N}$ with $m>n.\ $Then a proper submodule $P$ of $M\ $is said to be an $(m,n)$-semiprime submodule if $a^{m}x\in P\ $for some $a\in A,x\in M,\ $then $a^{n}x\in P.\ $Besides giving many characterizations and properties of this kind of submodules, we also use them to characterize von Neumann regular modules.