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Cyclic modules over fundamental rings derived from strongly regular equivalences. (English. French summary) Zbl 1390.16046

Summary: In this paper, we introduce and analyze a fundamental strongly regular equivalence relation on a hypermodule over a hyperring which is the smallest equivalence relation such that the quotient is cyclic module over a (fundamental) ring. Then we state the conditions that is equivalent with the transitivity of this relation. Finally, a characterization of the derived hypermodule (with canonical hypergroup) over a Krasner hyperring has been considered.

MSC:

16Y99 Generalizations
20N20 Hypergroups
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