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Naturally ordered regular semigroups with maximum inverses

Published online by Cambridge University Press:  20 January 2009

Tatsuhiko Saito
Tatsuhiko Saito
Affiliation:
Shimonoseki University of FisheriesYoshimi, Shimonoseki, Japan
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Let S be a regular semigroup. An inverse subsemigroup S° of S is called an inverse transversal if S° contains a unique inverse of each element of S. An inverse transversal S° of S is called multiplicative if x°xyy° is an idempotent of S° for every x, y∈S, where x° denotes the unique inverse of x∈S in S°. In Section 1, we obtain a necessary and sufficient condition in order for inverse transversals to be multiplicative.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 33 - 39
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

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