Relationship of Essentially Small Quasi-Dedekind Modules with Scalar and Multiplication Modules | Zendy

Inas Salman Obaid | Zendy; Mukdad Qaess Hussain | Zendy; Darya Jabar AbdulKareem | Zendy

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Relationship 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.

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