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On semigroup algebras

Published online by Cambridge University Press:  24 October 2008

W. D. Munn
W. D. Munn
Affiliation:
St John's CollegeCambridge
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Extract

In the classical theory of representations of a finite group by matrices over a field , the concept of the group algebra (group ring) over is of fundamental importance. The chief property of such an algebra is that it is semi-simple, provided that the characteristic of is zero or a prime not dividing the order of the group. As a consequence of this, the representations of the algebra, and hence of the group, are completely reducible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 1 - 15
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Albert, A. A.Structure of algebras (New York, 1939).CrossRefGoogle Scholar
(2)Clifford, A. H.Semigroups admitting relative inverses. Ann. Math., Princeton (2), 42 (1941), 1037–49.CrossRefGoogle Scholar
(3)Clifford, A. H.Matrix representations of completely simple semigroups. Amer. J. Math. 64 (1942), 327–42.CrossRefGoogle Scholar
(4)Clifford, A. H.Semigroups containing minimal ideals. Amer. J. Math. 70 (1948), 521–6.CrossRefGoogle Scholar
(5)Clifford, A. H.Semigroups without nilpotent ideals. Amer. J. Math. 71 (1949), 834–44.CrossRefGoogle Scholar
(6)Clifford, A. H. and Miller, D. D.Semigroups having zeroid elements. Amer. J. Math. 70 (1948), 117–25.CrossRefGoogle Scholar
(7)Green, J. A.On the structure of semigroups. Ann. Math., Princeton (2), 54 (1951), 163–72.CrossRefGoogle Scholar
(8)Jacobson, N.The theory of rings (New York, 1943).CrossRefGoogle Scholar
(9)Rees, D.On semi-groups. Proc. Camb. phil. Soc. 36 (1940), 387–400.CrossRefGoogle Scholar
(10)Teissier, M.Sur l'algèbre d'un demi-groupe fini simple. C.R. Acad. Sci., Paris, 234 (1952), 2413–14 and 2511–13.Google Scholar