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Homology and ringoids. II

Published online by Cambridge University Press:  24 October 2008

P. J. Hilton
Affiliation:
Department of MathematicsUniversity of Manchester
W. Ledermann
Affiliation:
Department of MathematicsUniversity of Manchester

Extract

1. Introduction and recapitulation. In a previous paper (4) we have defined a ringoid (with identities) as a set of elements α, β,… in which addition and multiplication are defined for certain pairs of elements in such a way that, whenever operations are defined, the usual ring axioms are satisfied. Precisely, is an abstract category ((3), p. 108) with an addition operation such that the following axioms hold:

(R 1) For any two identity elements ι, ι′ of, let ℋ(ι, ι′) be the set of elements ofwhose left identity is ι and right identity is ι′; then ℋ(ι, ι′) is empty or an Abelian group under addition.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

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