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Structure Theorems of a Module Over a Ring with a Bilinear Mapping

Published online by Cambridge University Press:  20 November 2018

Nobuo Nobusawa
Nobuo Nobusawa*
Affiliation:
University of Rhode Island
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Let R be a ring with an identity 1, and R′ a ring anti - isomorphic to R. Let V be an R-module as well as an R′-module. We assume that 1 a = a for all elements a in V and that V satisfies the minimum condition for R-submodules. Elements of R will be denoted by α, β, …, and those of V by a, b, … Elements of R′ will be a α′, β′, …, where α′ fcorresponds to α by the anti - isomorphism. A mapping f of V x V to R is called a bilinear mapping of V to R if it satisfies the following.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 5 , December 1967 , pp. 649 - 652
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Nobusawa, N., On a generalization of the ring theory. Osaka J. Math. vol. 1 (1966), 81-89.Google Scholar