Open AccessRelationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules
Author(s) -
Inas Salman Obaid,
Mukdad Qaess Hussain,
Darya Jabar AbdulKareem
Publication year - 2020
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.152
H-Index - 4
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2020.si.1.23
Subject(s) - scalar multiplication , mathematics , dedekind cut , prime (order theory) , scalar (mathematics) , pure mathematics , multiplication (music) , arithmetic , discrete mathematics , combinatorics , geometry
Let be a ring with 1 and D is a left module over . In this paper, we study the relationship between essentially small quasi-Dedekind modules with scalar and multiplication modules. We show that if D is a scalar small quasi-prime -module, thus D is an essentially small quasi-Dedekind -module. We also show that if D is a faithful multiplication -module, then D is an essentially small prime -module iff is an essentially small quasi-Dedekind ring.