Author:
Feller E. H.,Swokowski E. W.
Abstract
Characterizations for prime and semi-prime rings satisfying the right quotient conditions (see § 1) have been determined by A. W. Goldie in (4 and 5). A ring R is prime if and only if the right annihilator of every non-zero right ideal is zero. A natural generalization leads one to consider right R-modules having the properties that the annihilator in R of every non-zero submodule is zero and regular elements in R annihilate no non-zero elements of the module. This is the motivation for the definition of prime module in § 1.
Publisher
Canadian Mathematical Society
Cited by
24 articles.
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1. Strong -Submodules of a Module;Journal of Mathematics;2023-03-24
2. A generalization of Hartshorne's connectedness theorem;Boletim da Sociedade Paranaense de Matemática;2022-01-18
3. On the second spectrum of modules;Prykladni Problemy Mekhaniky i Matematyky;2021-12-22
4. On the Prime Spectrum of Torsion Modules;Iranian Journal of Mathematical Sciences and Informatics;2020-04-01
5. On radical formula in modules over noncommutative rings;Filomat;2020