Multiset Modules

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].