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Abstract. We study the ai-semiring variety defined by the identity $x^n\approx x$. We show that some subvarieties of this variety are determined by certain properties of some binary relations and provide equational basis for them. Also, we provide models of the free objects in some subvarieties of this variety.
DOI: 10.14232/actasm-021-164-8
AMS Subject Classification
(1991): 08B15, 08B20, 16Y60, 20M07
Keyword(s):
Burnside ai-semiring,
congruence,
free object,
lattice,
variety
received 15.1.2021, accepted 23.3.2021. (Registered under 164/2021.)
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