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Affine semigroups over an arbitrary field†

Published online by Cambridge University Press:  18 May 2009

W. Edwin Clark
W. Edwin Clark
Affiliation:
Tulane University and California Institute of Technology
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Let ℒ V denote the algebra of all linear transformations on an n-dimensional vector space V over a field Φ. A subsemigroup S of the multiplicative semigroup of ℒ V will be said to be an affine semigroup over Φ if S is a linear variety, i.e., a translate of a linear subspace of ℒ V.

This concept in a somewhat different form was introduced and studied by Haskell Cohen and H. S. Collins [1]. In an appendix we give their definition and outline a method of describing possibly infinite dimensional affine semigroups in terms of algebras and supplemented algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 2 , July 1965 , pp. 80 - 92
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

REFERENCES

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