Terms that are self-dual in Boolean algebras but not in MO 2 |
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Authors: | David Kelly R. Padmanabhan |
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Affiliation: | (1) Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2 |
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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 defines Boolean algebras modulo orthomodular lattices. (The dual of p is denoted by .) 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. |
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Keywords: | 2000 Mathematics Subject Classification: Primary 06C15 Secondary 08B05 |
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