On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules

Authors

  • Elhadji Demba Wade Diop Université Cheikh Anta Diop de Dakar

Keywords:

semiring, subsemimodule, $R$-congruence relation, essential, cancellative, subtractive, direct sum, cohopfian semimodules.

Abstract

Two different notions of "essential" subsemimodules were introduced
in the theory of semimodules over a semiring with identity, in order
to generalize the same notion of "essential" submodules in the
theory of modules over a ring with identity.


In this paper, we introduce a new class of essential subsemimodules
called weakly essential subsemimodules. We prove that this new class
contains the others two kind of classes of "essential"
subsemimodules. Futhermore, we studie the properties of weakly
essential subsemimodules. For applications we introduce and
investigate the co-hopfian semimodules with this new definition of
semi-essential.

Author Biography

  • Elhadji Demba Wade Diop, Université Cheikh Anta Diop de Dakar
    Dakar

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Published

2016-07-02

Issue

Vol. 9 No. 3: (July 2016)

Section

Algebra

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How to Cite

On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules. (2016). European Journal of Pure and Applied Mathematics, 9(3), 250-265. https://www.ejpam.com/index.php/ejpam/article/view/2562