A Property of the Weak Subalgebra Lattice for Algebras with Some Non-Equalities
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Let A be a locally finite total algebra of finite type such that kA(a1,...,an) ≠ai for every operation kA, elements a1,..., an and 1 ≤i≤ 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.
Abstract
Let A be a locally finite total algebra of finite type such that kA(a1,...,an) ≠ai for every operation kA, elements a1,..., an and 1 ≤i≤ 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.
참고문헌 (16)
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