Department of Mathematics
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We present independent self-dual equational bases of arbitrarily large finite sizes for the equational theory of groups, inverse semigroups, squags and lattices. In groups, the dual of a term \(f \) is the mirror reflection of \(f \) . For each variety of algebras, we provide an independent self-dual equational basis with \(n \) identities for \(n = 2,\, 3,\, 4\). Then we develop a simple algorithmic procedure to construct independent self-dual equational bases of arbitrary finite sizes in such a way that the new larger equational bases depend explicitly on the initial bases. Apart from generalizing the various theorems of Alfred Tarski who initiated this topic in the late 1960's, our proofs aso provide explicitly the equational bases and hence may be construed as the first constructive proof of Tarski's theorem as well. This work was done in collabration with William McCune and David Kelly.

References:

1. Kelly, David; Padmanabhan, R; Irredundant self-dual bases for self-dual lattice varieties, Algebra Universalis 52 (2004), no. 4, 501–517 (2005)
2. Tarksi, A.; Equational logic and equational theories of algebras, Contributions to Mathematics. North-Holland, 1968