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A Property of the Weak Subalgebra Lattice for Algebras with Some Non-Equalities

Pioro, Konrad

  • Received : 2008.07.09
  • Accepted : 2009.10.09
  • Published : 2010.06.30

Abstract

Let A be a locally finite total algebra of finite type such that $k^A(a_1,\cdots,a_n)\;{\neq}\;a_i$ ai for every operation $k^A$, elements $a_1,\cdots,a_n$ an and $1\;\leq\;i\;\leq\;n$. We show that the weak subalgebra lattice of A uniquely determines its (strong) subalgebra lattice. More precisely, for any algebra B of the same finite type, if the weak subalgebra lattices of A and B are isomorphic, then their subalgebra lattices are also isomorphic. Moreover, B is also total and locally finite.

Keywords

hypergraph;strong and weak subalgebras;subalgebra lattices;partial algebra

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  2. Subalgebra lattices of a partial unary algebra vol.45, pp.4, 2012, https://doi.org/10.1515/dema-2013-0416