On some strongly algebraically closed semirings

Article type: Research Article

Authors: Molkhasi, Ali^*

Affiliations: Department of Mathematics, Faculty of Mathematical Sciences, University of Farhangian-Iran

Correspondence: [*] Corresponding author. Ali Molkhasi, Department of Mathematics, Faculty of Mathematical Sciences, University of Farhangian-Iran. E-mail: [email protected].

Abstract: In the present paper, we introduce the notion of q′-compact in Łukasiewicz near semirings and we prove that if induced lattice with an antitone involution of a Łukasiewicz near semiring is a complete lattice and q′-compact, then the induced lattice is a strongly algebraically closed lattice. Also, it is shown that every Łukasiewicz near semiring is representable as a Sheffer stroke basic algebra. In the final part of the article, we prove that the variety of Sheffer stroke basic algebras is congruence regular and arithmetical.

Keywords: Sheffer Stroke basic algebra, strongly algebraically closed algebra, Łukasiewicz near semirings

Keywords: 06D36, 06E05, 13L05

DOI: 10.3233/JIFS-182661

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6393-6400, 2019