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Quasi-codivisible covers

Published online by Cambridge University Press:  17 April 2009

Paul E. Bland
Paul E. Bland
Affiliation:
Wallace 402, Eastern Kentucky University, Richmond, Kentucky 40475, U.S.A.
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Abstract

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In this paper quasi-codivisible covers are defined and investigated relative to a torsion theory (T, F) on Mod R. It is shown that if (T, F) is cohereditary, then a right R-module M has a quasi-codivisible cover whenever it has a codivisible cover. Moreover, it is shown that if (T, F) is cohereditary, then the universal existence of quasi-codivisible covers implies that the ring R/T (R) must be right perfect. The converse holds when (T, F) is pseudo-hereditary.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 389 - 395
Copyright
Copyright © Australian Mathematical Society 1986

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