The variety generated by semi-Heyting chains (Q432182)

The purpose of the paper is to investigate the properties of semi-Heyting chains and the structure of the variety generated by all semi-Heyting chains. The authors prove some results on semi-Heyting chains and determine the number of non-isomorphic structures of semi-Heyting algebra that can be defined over an \(n\)-element chain. They investigate the behaviour of the subalgebras of a given semi-Heyting chain. Finally, the authors find equational bases for many subvarieties of the variety generated by all semi-Heyting chains. Some open problems from a paper of \textit{H. P. Sankappanavar} [in: Actas del IX congreso de matemática ``Dr. Antonio A. R. Monteiro''. Bahía Blanca: Universidad Nacional del Sur, Instituto de Matemática. 33--66 (2008; Zbl 1175.06003)] are solved. I think that this article contains valuable results and may be a starting point for other studies on this subject.