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INTRODUCTION TO S-HOPFIAN AND S-CO-HOPFIAN

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 have 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 their properties. Additionally, we give some new variants of Fitting’s lemma which are already known on semimodules.


Auteur(s) : LANDING FALL, JEAN RAOUL TSIBA, DJIBY SOW
Pages : Pages 93-121
Année de publication : 2011
Revue : JP Journal of Algebra, Number Theory and Applications
N° de volume : Volume 22, Number 1
Type : Article
Statut Editorial : Journal
Mise en ligne par : FALL Landing