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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Strongly extending semimodules over a semiring

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pp. 1677–1687Vol. 27Issue 5August 2024DOI: 10.47974/JDMSC-2009 Crossmark XML
Received:
10 Jan 2024
Published Online:
26 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2009
Pages:
1677–1687

Abstract

In this work, the concept of strongly extending modules has been introduced for semimodules category. We call a semimodule C is strongly extending if for each subsemimodule A in C there is a stable direct summand B of C such that A is essential in B. Various characterizations of strongly extending semimodules are obtained. It is discussed direct sum property for strongly extending semimodules and gives more than results which this property is valid. Also, we provide many results concerned with the hereditary property for extending semimodules. A useful sufficient condition is given for the equivalence between extending and strongly extending semimodules. Further, we get a partial relation between extending semimodules and subtractive semimodules. 

Keywords

SemiringSemimoduleStrongly extending semimoduleSubtractive semimodules

Subject Classifications

16Y6006F25

References

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