Multiset Modules

Sunil Jacob  John; Suma  P; Athira T.M.

doi:10.47852/bonviewJCCE6152118205514

Authors

Sunil Jacob John Department of Mathematics, National Institute of Technology Calicut, India
Suma P Department of Mathematics, National Institute of Technology Calicut, India
Athira T.M. Department of Mathematics, National Institute of Technology Calicut, India https://orcid.org/0000-0001-5358-233X

DOI:

https://doi.org/10.47852/bonviewJCCE6152118205514

Keywords:

multiset module, multiset homomorphism, multiset isomorphism

Abstract

Multiset modules and their properties are introduced in this paper. Some interesting properties are obtained, such as the countable intersection of multiset modules is multiset module, but the union need not be. Also, the sub-multiset module is defined and illustrated with suitable examples. Homomorphism and isomorphism in the contest of multisets are defined, and some valuable theorems are proved. Then the quotient module is proposed, and the relation that M/ker f is isomorphic to Im f for a multiset homomorphism f. Multiset modules drawn from a ℤ module are of particular interest and proved that if L ∈ ML[ℤM], then L is an mset group under addition, and conversely, every mset abelian group drawn from ℤ is an element of ML[ℤM].

Received: 3 December 2021 | Revised: 21 January 2022 | Accepted: 31 January 2022

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.