The Variety of Semi-Heyting Algebras Satisfying the Equation (0 → 1)* V (0 → 1)** ≈ 1

Manuel Abad,

Juan Manuel Cornejo,

José Patricio Díaz Varela


In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity(0 - 1)* v (0 - 1)** = 11. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We also determine the sublattice generated by the subvarieties introduced in [4, Definition 8.1] within the lattice of subvarieties of semi-Heyting algebras.

[1] M. Abad, J.M. Cornejo and J.P. Diaz Varela, The Variety Generated by SemiHeyting Chains, submitted for publication.
[2] R. Balbes and P.H. Dwinger, Distributive lattices, University of Missouri Press, Columbia, 1974.
[3] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics 78, Springer-Verlag, New York, 1981.
[4] H.P. Sankappanavar, Semi-Heyting Algebras: An Abstraction From Heyting Algebras. Actas del IX Congreso A. Monteiro, Bah´ıa Blanca, 2007, pp. 33–66.

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