{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:00:33Z","timestamp":1777705233691,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,9,15]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3233\/jifs-211130","type":"journal-article","created":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T10:59:09Z","timestamp":1627037949000},"page":"3715-3726","source":"Crossref","is-referenced-by-count":2,"title":["New definition of MV-semimodules"],"prefix":"10.1177","volume":"41","author":[{"given":"Simin Saidi","family":"Goraghani","sequence":"first","affiliation":[{"name":"Department of Mathamatics, Farhangian University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rajab","family":"Ali Borzooei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Facultyof Mathematical Sciences, Shahid Beheshti University, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sun 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