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N-th root rings

Published online by Cambridge University Press:  17 April 2009

Henry Heatherly  and
Altha Blanchet
Henry Heatherly
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisana 70504, United Stats of America.
Altha Blanchet
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisana 70504, United Stats of America.
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Abstract

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A ring for which there is a fixed integer n ≥ 2 such that every element in the ring has an n-th in the ring is called an n-th root ring. This paper gives numerous examples of diverse types of n-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutative n-th root ring with unity. The structure of n-th root rings with chain conditions is developed and finite n-th root rings are completely classified. Subdirect product representations are given for several classes of n-th root rings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 111 - 123
Copyright
Copyright © Australian Mathematical Society 1987

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