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Polynomially Defined 𝑑-algebras and Connections with β-algebras
Akbar Rezaei and Hee Sik Kim
In this paper, we introduce a notion of 𝐾-nonvanishing map on a field 𝐾, and we obtain polynomially defined 𝑑-algebras which are not 𝐵𝐶𝐾 algebras, as well as some conditions for these to be strong 𝑑-algebras. Moreover, we investigate some relations between polynomially defined 𝑑-algebras with left-zero semigroups and β-algebras.
2020 Mathematics Subject Classification. 06F35, 20N02.
Keywords: (Strong) d-algebra, β-algebra, K-nonvanishing, polynomially defined d-algebra