Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-03T05:42:56.045Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1.Cohen, Haskell and Collins, H. S., Affine semigroups, Trans. Amer. Math. Soc. 93 (1959), 97–113.CrossRefGoogle Scholar
2.Collins, H. S., Remarks on affine semigroups, Pacific Journal of Mathematics 12, no. 2, (1962), 449–455.CrossRefGoogle Scholar
3.Wallace, A. D., Remarks on affine semigroups, Bull. Amer. Math. Soc. 66 (1960), 110–112.CrossRefGoogle Scholar
4.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. I (Math. Surveys No. 7, American Mathematical Society, Providence, 1961).Google Scholar
5.Jacobson, N., Structure of rings (American Mathematical Society Colloquium Publication, Vol. XXXVII, Providence, 1956).Google Scholar
6.Mirsky, L., An introduction to linear algebra (Oxford, 1955).Google Scholar
7.Drazin, M. P., Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514.CrossRefGoogle Scholar
8.Munn, W. D., Pseudo-inverses in semigroups, Proc. Cambridge Philos. Soc. 57 (1961), 247–250.CrossRefGoogle Scholar
9.Clark, W. E., Remarks on minimal ideals in matrix semigroups, Czechoslovak Math. J. (to appear).Google Scholar
10.Cartan, H. and Eilenberg, S., Homological algebra, (Princeton Mathematical Surveys 19, Princeton, New Jersey, 1956).Google Scholar