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akadeemia kirjastus
SINCE 1952
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of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
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On (mn)-semiprime submodules; pp. 260–267
PDF | 10.3176/proc.2021.3.05

Ayten Pekin, Suat Koç, Emel Aslankarayiğit Uğurlu

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


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