New definition of MV-semimodules

Article type: Research Article

Authors: Goraghani, Simin Saidi^a | Ali Borzooei, Rajab^b | Ahn, Sun Shin^{c; *}

Affiliations: [a] Department of Mathamatics, Farhangian University, Tehran, Iran | [b] Department of Mathematics, Facultyof Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | [c] Department of Mathematics Education, DonggukUniversity, Seoul, Korea

Correspondence: [*] Corresponding author. Sun Shin Ahn, Department of Mathematics Education, Dongguk University, Seoul 04620, Korea. E-mail: sunshine@dongguk.edu.

Abstract: In recent years, A. Di Nola et al. studied the notions of MV-semiring and semimodules and investigated related results [9, 10, 12, 26]. Now in this paper, by using an MV-semiring and an MV-algebra, we introduce the new definition of MV-semimodule, study basic properties and find some examples. Then we study A-ideals on MV-semimodules and Q-ideals on MV-semirings, and by using them, we study the quotient structures of MV-semimodule. Finally, we present the notions of prime A-ideal, torsion free MV-semimodule and annihilator on MV-semimodule and we study the relations among them.

Keywords: MV-semiring, MV-algebra, MV-module, MV-semimodule, Q-ideal, prime A-ideal

Keywords: 06D35, 16Y60

DOI: 10.3233/JIFS-211130

Journal: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 2, pp. 3715-3726, 2021