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

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 2,  2010, pp.195-211
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.2.195
Title & Authors
A Property of the Weak Subalgebra Lattice for Algebras with Some Non-Equalities

Abstract
Let A be a locally finite total algebra of finite type such that $\small{k^A(a_1,\cdots,a_n)\;{\neq}\;a_i}$ ai for every operation $\small{k^A}$, elements $\small{a_1,\cdots,a_n}$ an and $\small{1\;\leq\;i\;\leq\;n}$. 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;
Language
English
Cited by
1.
A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE, International Journal of Algebra and Computation, 2013, 23, 01, 1
2.
Subalgebra lattices of a partial unary algebra, Demonstratio Mathematica, 2012, 45, 4
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