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The Torsion Submodule of A Cyclic Module Splits Off

Published online by Cambridge University Press:  20 November 2018

Mark L. Teply
Mark L. Teply*
Affiliation:
University of Florida, Gainesville, Florida
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A prominent question in the study of modules over an integral domain has been: “When is the torsion submodule t(A) of a module A a direct summand of A?” A module is said to split when its torsion module is a direct summand. Clearly, every cyclic module over an integral domain splits. Interesting splitting problems have been explored by Kaplansky [14; 15], Rotman [20], Chase [4], and others.

Recently, many concepts of torsion have been proposed for modules over arbitrary associative rings with identity. Two of the most important of these concepts are Goldie's torsion theory (see [1; 12; 22]) and the simple torsion theory (see [5; 6; 8; 9; 23], and their references).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 3 , June 1972 , pp. 450 - 464
Copyright
Copyright © Canadian Mathematical Society 1972

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