Vol. 91, No. 2, 1980

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Dimension modules

Victor P. Camillo and Julius Martin Zelmanowitz

Vol. 91 (1980), No. 2, 249–261
Abstract

M is called a dimension module if d(A + B) = d(A) + d(B) d(A B) holds for all submodules A and B of M, where d(M) denotes the Goldie (uniform) dimension of a module M. We characterize these modules as the modules which have no submodules of the form X X∕Y with Y an essential submodule of X. As a test, the structure of a completely decomposable injective dimension module is determined.

Mathematical Subject Classification
Primary: 16A53, 16A53
Milestones
Received: 28 November 1978
Revised: 12 November 1979
Published: 1 December 1980
Authors
Victor P. Camillo
Julius Martin Zelmanowitz