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Terms that are self-dual in Boolean algebras but not in MO 2
Authors:David Kelly  R. Padmanabhan
Affiliation:(1) Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2
Abstract:
An absorption law is an identity of the form p = x. The ternary function x+y+z (ring addition) in Boolean algebras satisfies three absorption laws in two variables. If a term satisfies these three identities in a variety, it is called a minority term for that variety. We construct a minority term p for orthomodular lattices such the identity $$p = tilde{p}$$ defines Boolean algebras modulo orthomodular lattices. (The dual of p is denoted by $$tilde{p}$$.) Consequently, having a unique minority term function characterizes Boolean algebras among orthomodular lattices. Our main result generalizes this example to arbitrary arity and arbitrary consistent sets of 2-variable absorption laws. Presented by J. Berman.
Keywords:2000 Mathematics Subject Classification: Primary 06C15  Secondary 08B05
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