Vol. 65, No. 2, 1976

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Regular and semisimple modules

T. J. Cheatham and J. R. Smith

Vol. 65 (1976), No. 2, 315–323

A module is regular if all its submodules are (Cohn) pure. The family of all regular modules is closed under products if and only if R∕J(R) is a von Neumann regular ring. If each regular R-module is semisimple then R is a T-ring. An extra condition is needed for the converse. Character modules and extensions of regular and semisimple modules are investigated.

Mathematical Subject Classification
Primary: 16A64, 16A64
Received: 18 March 1974
Published: 1 August 1976
T. J. Cheatham
J. R. Smith