$(L\)-Modules$

(L\)-Modules

In this paper, considering $L$-algebras, which include a significant number of other algebraic structures, we present a definition of modules on $L$-algebras ($L$-modules). Then we provide some examples and obtain some results on $L$-modules. Also, we present definitions of prime ideals of \...

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Veröffentlicht in:	Bulletin of the Section of Logic 2024, Vol.53 (1), p.125-144
Hauptverfasser:	Saidi Goraghani, Simin, Borzooei, Rajab Ali
Format:	Artikel
Sprache:	eng
Schlagworte:	Logic
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this paper, considering $L$-algebras, which include a significant number of other algebraic structures, we present a definition of modules on $L$-algebras ($L$-modules). Then we provide some examples and obtain some results on $L$-modules. Also, we present definitions of prime ideals of $L$-algebras and $L$-submodules (prime $L$-submodules) of $L$-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime $L$-submodules.
ISSN:	0138-0680 2449-836X

Zusammenfassung:	In this paper, considering \(L\)-algebras, which include a significant number of other algebraic structures, we present a definition of modules on \(L\)-algebras (\(L\)-modules). Then we provide some examples and obtain some results on \(L\)-modules. Also, we present definitions of prime ideals of \(L\)-algebras and \(L\)-submodules (prime \(L\)-submodules) of \(L\)-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime \(L\)-submodules.
ISSN:	0138-0680 2449-836X