On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules
Keywords:
semiring, subsemimodule, $R$-congruence relation, essential, cancellative, subtractive, direct sum, cohopfian semimodules.Abstract
Two different notions of "essential" subsemimodules were introducedin 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.
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Published
2016-07-02
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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://ejpam.com/index.php/ejpam/article/view/2562