Vol. 40, No. 1, 1972

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Neat homomorphisms

James J. Bowe

Vol. 40 (1972), No. 1, 13–21

The study of neat homomorphisms found in this paper originated with a generalization of neat subgroups and a property of torsion free coverings studied by Enochs. Several useful characterizations and properties of neat homomorphisms are shown leading to the characterization of various rings. A ring is hereditary if and only if each component of the natural decomposition of a neat homomorphism is neat. Furthermore, a ring is NQetherian if and only if the direct sum (and direct limit) of a family of neat homomorphisms is neat. For the singular torsion theory, every non-zert) torsion module contains a simple submodule if and only if the product of a family of neat homomorphisms is neat. If R has zero singular ideal and zero left socle, then the singular theory coincides with the simple theory if and only if the above condition is true.

Mathematical Subject Classification
Primary: 16A64
Received: 6 October 1970
Published: 1 January 1972
James J. Bowe