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Introduction to S -Hopfian and S -co-Hopfian semimodules.

The theory of semimodules and semirings, regarded as a generalized theory of rings and modules, is widely studied since 1956. In module theory, the notions of Hopfian and Co-Hopfian on modules and the notions of $I$-ring and $S$-ring has been extensively studied by many researchers. As an analogue to module theory, in this paper, we introduce the notions of S-Hopfian and S-Co-Hopfian on subtractive semimodules over semirings and we study also some of there properties. Additionally, we give some new variants of Fitting's lemma which is already known on semimodules .


Auteur(s) : Jean Raoul; Sow, Djiby and Fall, Landing
Pages : 81–109
Année de publication : 2011
Revue : JP J. Algebra Number Theory Appl.
N° de volume : 22
Type : Article
Mise en ligne par : SOW Djiby