Relation algebras and groups
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DOI: 10.1007/s00012-018-0505-0
Abstract: Generalizing results of Jónsson and Tarski, Maddux introduced the notion of a pair-dense relation algebra and proved that every pair-dense relation algebra is representable. The notion of a pair below the identity element is readily… read more here.
Keywords: algebra; relation algebras; relation; notion ... See more keywords
Representability of Lyndon–Maddux relation algebras
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DOI: 10.1007/s00012-018-0536-6
Abstract: In 2016, Alm–Hirsch–Maddux defined relation algebras $$\mathfrak {L}(q,n)$$L(q,n) that generalize Roger Lyndon’s relation algebras from projective lines, so that $$\mathfrak {L}(q,0)$$L(q,0) is a Lyndon algebra. In that paper, it was shown that if $$q>2304n^2+1$$q>2304n2+1, then… read more here.
Keywords: maddux relation; mathfrak representable; relation algebras; relation ... See more keywords
Varieties generated by completions
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DOI: 10.1007/s00012-019-0602-8
Abstract: We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation algebras… read more here.
Keywords: generated completions; persistently finite; relation algebras; variety generated ... See more keywords