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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.
Perspectives
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.
Dr Ali Molkhasi
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This page is a summary of: On some strongly algebraically closed semirings, Journal of Intelligent & Fuzzy Systems Applications in Engineering and Technology, June 2019, IOS Press,
DOI: 10.3233/jifs-182661.
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