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Reflection-closed varieties of multisorted algebras and minor identities

Lehtonen, Erkko; Pöschel, Reinhard; Waldhauser, Tamás

Algebra Universalis, 79 (2018), Art. 70, 22 pp.

The notion of reflection is considered in the setting of multisorted algebras. The Galois connection induced by the satisfaction relation between multisorted algebras and minor identities provides a characterization of reflection-closed varieties: a variety of multisorted algebras is reflection-closed if and only if it is definable by minor identities. Minor-equational theories of multisorted algebras are described by explicit closure conditions. It is also observed that nontrivial varieties of multisorted algebras of a non-composable type are reflection-closed.