A generalization of torsion to modules

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Frances Ann Bennett (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Robert Bernhardt

Abstract: The concepts of torsion and torsion-free objects have their origins in abelian group theory, where for an abelian group G the torsion subgroup T(G) of G is defined by T(G) = {x ? G | there exists a positive integer n such that nx = 0}, and where G is torsion-free provided T(G) = 0. Several ways of generalizing these notions to the category RM of left R-modules over a ring are known. In [3] Dickson defines the concept of a torsion theory for certain abelian categories which include RM, and this definition encompasses most of the standard generalizations of torsion and torsion-free in RM. We shall study these torsion theories in RM rather than in the more general setting in which R they originally appeared.

Additional Information

Language: English
Date: 1971
Torsion theory (Algebra)
Modules (Algebra)

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