Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 6، دوره 2، شماره 1، مهر 2014، صفحه 65-82 اصل مقاله (511.92 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Hanamantagouda P. Sankappanavar | ||
| Department of Mathematics, State University of New York, New Paltz, NY 12561 | ||
| چکیده | ||
| This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--the latter is known to be generated by the expansions of the three 4-element Boolean semi-Heyting algebras. As consequences of our main theorem, we present (equational) axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The paper concludes with some open problems for further investigation. | ||
| کلیدواژهها | ||
| Regular dually quasi-De Morgan semi-Heyting algebra of level 1؛ dually pseudocomplemented semi-Heyting algebra؛ De Morgan semi-Heyting algebra؛ strongly blended dually quasi-De Morgan Stone semi-Heyting algebra؛ discriminator variety؛ simple؛ directly indecomposable؛ subdirectly irreducible؛ equational base | ||
| مراجع | ||
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