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Butler Modules Over Valuation Domains

Published online by Cambridge University Press:  20 November 2018

L. Fuchs  and
E. Monari-Martinez
L. Fuchs
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 U S. A.
E. Monari-Martinez
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 U S. A.
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Let R be a commutative domain with 1, Q its field of quotients, and M a torsion-free R module. By a balanced submodule of M is meant an RD-submodule N [i.e. rN = N ∩ rM for each r ∈ R] such that, for every R-submodule J of Q, every homomorphism η : J → M/N can be lifted to a homomorphism χ:J → M. This definition extends the notion of balancedness as introduced in abelian groups (see e.g. [10, p. 113]). The balanced-projective R-modules can be characterized as summands of completely decomposable R-modules (i.e. summands of direct sums of submodules of Q). If R is a valuation domain, then such summands are again completely decomposable; see [12, p. 275].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 1 , 01 February 1991 , pp. 48 - 60
Copyright
Copyright © Canadian Mathematical Society 1991

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