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http://dx.doi.org/10.5666/KMJ.2010.50.2.195

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

Pioro, Konrad (Institute of Mathematics, University of Warsaw)
Publication Information
Kyungpook Mathematical Journal / v.50, no.2, 2010 , pp. 195-211 More about this Journal
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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