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TZID:Europe/Budapest
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UID:78feid5pb6t6cbmmtpj9pc0j7l@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Ágnes Szendrei (University of Boulder): Idempotent Linear Maltsev Conditions: Can We Find Interesting Models by Random Search?
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:
Abstract.
Let L be a finite algebraic language with at least
one operation symbol of arity >1. By a result of Murskii (1975), a random f
inite L-algebra is almost surely a semiprimal algebra with no proper subalg
ebras of size >1. In a recent joint paper with Cliff Bergman (2018+) we loo
ked at the analogous problem when the probability space is restricted to th
e class of all finite models of a set M of idempotent linear L-identities,
i.e., the identities of a strong, idempotent, linear Maltsev condition. We
found a simple syntactic condition (*) such that M satisfies (*) if and onl
y if a random finite model of M is almost surely idemprimal.
I wil
l start the talk by reviewing this result, and then I will discuss the foll
owing question: Which clones occur with positive probability among the clon
es of random finite models of M? Clearly, this question is interesting only
if (*) fails for M; this is the case, for example, if M is the set of iden
tities for a Maltsev term, or majority term, or minority term, or semiproje
ction term.
DTSTAMP:20240328T212308Z
DTSTART;TZID=Europe/Budapest:20190605T100000
DTEND;TZID=Europe/Budapest:20190605T110000
SEQUENCE:0
TRANSP:OPAQUE
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