ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 68,   2   (1999)
pp.   295-318
REGULARISING NATURAL DUALITIES
B. A. DAVEY and B. J. KNOX

Abstract.  Given an algebra $\mbfM$ we may adjoin an isolated zero to form an algebra $\infM$ satisfying all identities $u \approx v$ true in $\mbfM$ for which $u$ and $v$ contain the same variables. Drawing on the structure theory of P\l onka sums, we show that if $\mbfM$ is a finite, dualisable algebra which is strongly irregular, then $\infM$ is also dualisable. Turning the construction of $\infM$ upside-down for the two-element left-zero band, we exhibit a duality for quasi-regular left-normal bands.

AMS subject classification.  08C05, 20M30; Secondary 18A40
Keywords.  natural duality, P\l onka sum, regularisation, quasi-regularisation, left-normal semigroup
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