On hereditary torsion theories

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

Abstract: This thesis deals with S. E. Dickson's concept of a hereditary torsion theory for the category RM of left R-modules over an arbitrary ring R. It is proved that a class of left R-modules is a hereditary torsion class if and only if there is an injective module which generates it. A method is given for generating a torsion-torsionfree class from a projective module. Further, it is proved that if R is a semi-perfect ring, then under certain conditions a torsion-torsionfree class is generated by a projective module. A characterization of a hereditary torsion class in terms of a module X uniquely determined by the elements of the torsion filter is given. It is proved that there is a one-to-one correspondence between the two-sided, idempotent ideals of R and the torsion-torsionfree classes for RM. The thesis concludes with the definition of a centrally splitting torsion theory, and with the proof that there is a one-to-one correspondence between the central idempotents of R and the centrally splitting torsion theories for RM.

Additional Information

Language: English
Date: 1973
Torsion theory (Algebra)
Torsion free Abelian groups

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