Vol. 40, No. 1, 1972

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The singular submodule of a finitely generated module splits off

John Fuelberth and Mark Lawrence Teply

Vol. 40 (1972), No. 1, 73–82
Abstract

A characterization is given of the finitely generated nonsingular left R-modules N such that ExtR1(N,M) = 0 for every singular left R-module M. As a corollary, the rings R, over which the singular submodule Z(A) is a direct summand of every finitely generated left R-module A, are characterized. This characterization takes on a simplified form whenever R is commutative. An example is given to show that a ring R, over which the singular submodule Z(A) is a direct summand of every left R-module A, need not be right semi-hereditary.

Mathematical Subject Classification
Primary: 16A64
Milestones
Received: 9 December 1970
Revised: 22 March 1971
Published: 1 January 1972
Authors
John Fuelberth
Mark Lawrence Teply