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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:\nAbstract.\n\nLet L be a finite algebraic language with at least one opera
tion symbol of arity >1. By a result of Murskii (1975), a random finite L-a
lgebra is almost surely a semiprimal algebra with no proper subalgebras of
size >1. In a recent joint paper with Cliff Bergman (2018+) we looked at th
e analogous problem when the probability space is restricted to the class o
f 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 s
imple syntactic condition (*) such that M satisfies (*) if and only if a ra
ndom finite model of M is almost surely idemprimal.\n\nI will start the tal
k by reviewing this result, and then I will discuss the following question:
Which clones occur with positive probability among the clones of random fi
nite models of M? Clearly, this question is interesting only if (*) fails f
or M; this is the case, for example, if M is the set of identities for a Ma
ltsev term, or majority term, or minority term, or semiprojection term.
DTSTAMP:20200926T003950Z
DTSTART;TZID=Europe/Budapest:20190605T100000
DTEND;TZID=Europe/Budapest:20190605T110000
SEQUENCE:0
TRANSP:OPAQUE
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