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Semiregular Modules and Rings

Published online by Cambridge University Press:  20 November 2018

W. K. Nicholson
W. K. Nicholson*
Affiliation:
University of Calgary, Calgary, Alberta
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Mares [9] has called a projective module semiperfect if every homomorphic image has a projective cover and has shown that many of the properties of semiperfect rings can be extended to these modules. More recently Zelmanowitz [16] has called a module regular if every finitely generated submodule is a projective direct summand. In the present paper a class of semiregular modules is introduced which contains all regular and all semiperfect modules. Several characterizations of these modules are given and a structure theorem is proved. In addition several theorems about regular and semiperfect modules are extended.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1105 - 1120
Copyright
Copyright © Canadian Mathematical Society 1976

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