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On congruences of finite multibasic universal algebras. (English. Russian original) Zbl 0970.08005
Discrete Math. Appl. 9, No. 4, 403-418 (1999); translation from Diskret. Mat. 11, No. 3, 48-62 (1999).
A multibasic algebra \((M,\omega)\) is defined as a special case of a heterogeneous algebra, i.e. it is \((A_1,\dots, A_n,A_0,\omega)\) where \(A_i\in M\) are nonempty sets and \(\omega\) is a mapping from \(A_1\times\cdots\times A_n\) into \(A_0\). A congruence is an equivalence \(\varepsilon\) on \(M\) satisfying the condition \[ \omega([a_1]\varepsilon(A_1),\dots, [a_n]\varepsilon(A_n))\subseteq [a_0]\varepsilon(A_0). \] The set of all such congruences need not form a lattice with respect to a natural ordering. The author studies maximal subsets of congruences which determine the whole set of these congruences. The majority of results is formulated for multibasic algebras derived from groups and quasigroups.
MSC:
08A68 Heterogeneous algebras
08A30 Subalgebras, congruence relations
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