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The Additive Group of an f-ring

Published online by Cambridge University Press:  20 November 2018

Paul Conrad
Paul Conrad*
Affiliation:
University of Kansas, Lawrence, Kansas
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The intent of this paper is to show that the additive l-group of an f-ring S determines the ring structure. This is why there are so many papers that simply extend known results for abelian l-groups to f-rings. Theorem 3.1 asserts that there is a one-to-one correspondence between the f-multiplications on S and a set of homomorphisms from the positive cone of the l-group S into the positive cone of the ring (S) of polar preserving endomorphisms of the l-group S. In fact, each f-multiplication of S is determined by a homomorphism of S+ into (S)+.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1157 - 1168
Copyright
Copyright © Canadian Mathematical Society 1974

References

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