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UID:2jcgjvtm50ndqkmaik9ovqftdu@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:Andreja Tepavcevic (University of Novi Sad and MI SANU Belgrade): Weak congruences, closure systems and lattice-valued structures
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Starting with Ω-sets where Ω is a complete lattice, we introduce
the notion of an Ω-algebra, which is a classical algebra equipped with an Ω
-valued equality replacing the ordinary one. In these new structures identi
ties hold as appropriate lattice-theoretic formulas. Identities hold in suc
h an algebra if and only if they hold on all particular cut-factor algebras
, i.e., cut subalgebras over cut-equalities. This approach is directly rela
ted to weak congruences of the basic algebra to which a generalized equalit
y is associated. Namely every Ω-algebra uniquely determines a closure syste
m in the lattice of weak congruences of the basic algebra. By this correspo
ndence we formulate a representation theorem for Ω-algebras. Some special c
lasses of such algebras will be elaborated as well as approach to varieties
of such algebras.\nThis is a join work with Branimir Seselja.
DTSTAMP:20230129T102544Z
DTSTART;TZID=Europe/Budapest:20190220T100000
DTEND;TZID=Europe/Budapest:20190220T120000
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