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IMPLICIT OPERATIONS ON FINITE J-TRIVIAL SEMIGROUPS AND A CONJECTURE OF SIMON,I.

Title
IMPLICIT OPERATIONS ON FINITE J-TRIVIAL SEMIGROUPS AND A CONJECTURE OF SIMON,I.
Type
Article in International Scientific Journal
Year
1991
Authors
ALMEIDA, J
(Author)
FCUP
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Journal
Vol. 69
Pages: 205-218
ISSN: 0022-4049
Publisher: Elsevier
Scientific classification
FOS: Natural sciences > Mathematics
Other information
Authenticus ID: P-001-R0C
Abstract (EN): Let J be the pseudovariety of all finite j-trivial semigroups and let OMEGABAR(n)J denote the topological semigroup of all n-ary implicit operations on J. The semigroup OMEGABAR(n)J is generated by the n component projections together with the 2n - 1 idempotents. Furthermore, OMEGABAR(n)J is described as a free algebra of type (1,2) in a certain variety and the word problem is solved in this algebra. As a consequence, OMEGABAR(n)J is countable, which settles a conjecture proposed by I. Simon.
Language: English
Type (Professor's evaluation): Scientific
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