Abstract
We investigate V-free algebras onn generators,F n =F r (V, n), where V is a discriminator variety and, more specifically, where V is a variety of relation algebras or of cylindricalgebras. Sample questions are: (a) IsF n+1 embeddable inF n ? (b) DoesF n contain an n-element set that generates it non-freely? The answer to (a) is affirmative in some varieties of relation algebras, but it is negative in every congruence extensile variety in which some nontrivial finite member is an absolute retract. The answer to (b) is affirmative in every variety of relation algebras that contains the full algebra of relations on an infinite set.
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Research supported by Hungarian National Foundation for Scientific Research grant No. 1810.
Research supported by NSF grant DMS-8800290.
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Andréka, H., Jónsson, B. & Németi, I. Free algebras in discriminator varieties. Algebra Universalis 28, 401–447 (1991). https://doi.org/10.1007/BF01191089
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DOI: https://doi.org/10.1007/BF01191089