Reflection-closed varieties of multisorted algebras and minor identities

Erkko Lehtonen, Reinhard Pöschel, Tamás Waldhauser

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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.

Original languageBritish English
Article number70
JournalAlgebra Universalis
Issue number3
StatePublished - 1 Sep 2018


  • Identities
  • Multisorted algebras
  • Reflections
  • Varieties


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