Open AccessOn a class of -modules
Author(s) -
Indah Emilia Wijayanti,
Muhammad Ardiyansyah,
Puguh Wahyu Prasetyo
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i3.513
Subject(s) - homomorphism , mathematics , commutative ring , lattice (music) , class (philosophy) , commutative property , pure mathematics , projective module , algebra over a field , multiplication (music) , discrete mathematics , combinatorics , computer science , physics , finitely generated abelian group , artificial intelligence , acoustics
UDC 512.5Smith in paper [ Mapping between module lattices, Int. Electron. J. Algebra, 15 , 173–195 (2014)] introduced maps between the lattice of ideals of a commutative ring and the lattice of submodules of an -module i.e., and mappings.The definitions of the maps were motivated by the definition of multiplication modules.Moreover, some sufficient conditions for the maps to be a lattice homomorphisms are studied.In this work we define a class of -modules and observe the properties of the class. We give a sufficient conditions for the module and the ring such that the class is a hereditary pretorsion class.