Abstract
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.
Résumé
Au cours de cet article, nous introduisons et analysons une relation d’équivalence fondamentale fortement réguliére sur un hypermodule sur un hyperanneau qui est la plus petite relation d’équivalence vérifiant la propriété que le quotient est un module cyclique sur un anneau (fondamental). Puis nous énonçons des conditions qui sont équivalentes á la transitivitéé de cette relation. Enfin, nous considérons aussi une caractérisation de l’hypermodule dérivé (avec l’hypergroupe canonique) sur un hyperanneau de Krasner.
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Mirvakili, S., Ghiasvand, P. & Davvaz, B. Cyclic modules over fundamental rings derived from strongly regular equivalences. Ann. Math. Québec 41, 265–276 (2017). https://doi.org/10.1007/s40316-016-0074-6
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DOI: https://doi.org/10.1007/s40316-016-0074-6