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Pseudo-inverses in Semigroups*

Published online by Cambridge University Press:  24 October 2008

W. D. Munn
W. D. Munn
Affiliation:
The University, Glasgow
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Extract

Drazin (2) has recently introduced the concept of a pseudo-invertible element of an associative ring or semigroup. In this note we first show that such an element of a semigroup S may be characterized by the fact that some power of it lies in a subgroup of S. The main result (Theorem 2) provides a new criterion for complete simplicity: a simple semigroup is completely simple if and only if all its elements are pseudo-invertible. This is applied to the principal factors of a general semigroup and two previously known results are obtained as corollaries.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 247 - 250
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

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