JP Journal of Algebra, Number Theory and Applications
Volume 22, Issue 1, Pages 81 - 109
(August 2011)
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INTRODUCTION TO S-HOPFIAN AND S-CO-HOPFIAN SEMIMODULES
Jean Raoul Tsiba, Djiby Sow and Landing Fall
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Abstract: 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. |
Keywords and phrases: modules, rings, subtractive semimodules, Hopfian, co-Hopfian, Fitting’s lemma. |
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