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Divisible S-systems and R-modules

Published online by Cambridge University Press:  20 January 2009

Victoria Gould
Victoria Gould
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, England
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Throughout this paper S will denote a given monoid and R a given ring with unity. A set A is a right S-system if there is a map φ:A × S→A satisfying

and

for any element a of A and any elements s, t of S. For φ(a, s) we write as and we refer to right S-systems simply as S-systems. One has the obvious definitions of an S-subsystem, an S-homomorphism and a congruence on an S-system. The reader ispresumed to be familiar with the basic definitions concerning right R-modules over R. As with S-systems we will refer to right R-modules just as R-modules.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 2 , June 1987 , pp. 187 - 200
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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