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.
| Original language | English |
|---|---|
| Pages (from-to) | 3715-3726 |
| Number of pages | 12 |
| Journal | Journal of Intelligent and Fuzzy Systems |
| Volume | 41 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2021 |
Keywords
- MV-algebra
- MV-module
- MV-semimodule
- MV-semiring
- prime A-ideal
- Q-ideal