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Semigroups with Quasi-Zeroes

Published online by Cambridge University Press:  20 November 2018

S. A. Rankin  and
C. M. Reis
S. A. Rankin
Affiliation:
University of Western Ontario, London, Ontario
C. M. Reis
Affiliation:
University of Western Ontario, London, Ontario
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Let S be a semigroup. An element a ∈ S is said to be a left quasi-zero if <a>x ⋂ <a> ≠ ∅ for all x ∈ S, where <a> denotes the cyclic sub-semigroup of S generated by a. In a recent study [6] of semigroups with a maximum right congruence, such elements proved to be useful in providing characterizations of these semigroups. Left quasizeroes have appeared in the literature under different names in a variety of situations. In the context of semigroup radicals, left quasi-zeroes are called right quasi-regular elements, where an element is defined to be right quasi-regular if it is not a left identity for any right congruence other than the universal congruence (see [4], [5], [2], [7], and [8]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 3 , 01 June 1980 , pp. 511 - 530
Copyright
Copyright © Canadian Mathematical Society 1980

References

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