Original Articles

HOMOGENEOUS FUNCTIONS DETERMINED BY CYCLIC SUBMODULES

Published in: Quaestiones Mathematicae
Volume 21 , issue 3-4 , 1998 , pages: 219–234

DOI: 10.1080/16073606.1998.9632042

Author(s): C.J. Maxson Department of Mathematics, USA , J.H. Meyer Department of Mathematics, Republic of South Africa

Keywords: Primary 13C99 , 13F10 , Secondary 16Y30

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Abstract

For a unital module V over a commutative ring R, let C denote the collection of cyclic submodules. The ring ϵ_R(V;C) = {f ε End_R V |f(C) ⊆C, ∀C ε_R (V;C) has been the object of several recent studies in which the structure of ϵ_R(V;C) is related to the triple (V, R,C). Here we introduce a new ring H_R(V;C) containing ϵ(V;C) and investigate its structure in terms of the parameters (V, R, C).

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