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The algebra of mode homomorphisms. (English) Zbl 1312.08001
A mode is an algebra in which every singleton is a subalgebra and every operation is a homomorphism (all operations commute). Both properties can be formulated as satisfying some identities in an algebra. In this paper, algebras of mode homomorphisms are introduced and studied in detail. They are constructed as follows: for modes in a prevariety $$K$$ of modes of given (plural) type $$\tau\colon\Omega\to\mathbb Z_+$$, one considers the set of all homomorphisms from subalgebras of one mode to subalgebras of another with operations from $$\Omega$$ defined in a special but natural way to obtain again an algebra in $$K$$.

##### MSC:
 08A05 Structure theory of algebraic structures 06A12 Semilattices
##### Keywords:
modes; semilattices; variety regularizations; Płonka sums
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##### References:
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