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Lattice-ordered modules of quotients

Part of: Ordered structures

Published online by Cambridge University Press:  09 April 2009

Stuart A. Steinberg
Stuart A. Steinberg
Affiliation:
University of Toledo, Toledo, Ohio 43606, U.S.A.
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Abstract

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Let Q be the ring of quotients of the f-ring R with respect to a positive hereditary torsion theory and suppose Q is a right f-ring. It is shown that if the finitely-generated right ideals of R are principal, then Q is an f-ring. Also, if QR is injective, Q is an f-ring if and only if its Jacobson radical is convex. Moreover, a class of po-rings is introduced (which includes the classes of commutative po-rings and right convex f-rings) over which Q(M) is an f-module for each f-module M.

MSC classification

Secondary: 06F25: Ordered rings, algebras, modules

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 243 - 251
Copyright
Copyright © Australian Mathematical Society 1980

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