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Note on strongly regular near-rings

Published online by Cambridge University Press:  20 January 2009

Motoshi Hongan
Motoshi Hongan
Affiliation:
Tsuyama College of Technology, Numa, Tsuyama, Okayama, Japan
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Let S be a semigroup. An element a of S is called right (resp. left) regular if a=a2x (resp. a=xa2) for some x∈S. If a is regular and right (resp. left) regular, a is called strongly right (resp. left) regular. As is well known, if a is strongly regular (i.e., right and left regular) then it is regular, more precisely, there exists uniquely an element x such that a= a2x,x= x2a and ax=xa, and a is contained in a subgroup of S (and conversely).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 379 - 381
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

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