Advances and Applications in Discrete Mathematics
Volume 14, Issue 1, Pages 25 - 38
(July 2014)
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A CHARACTERIZATION OF ALL ALGEBRAS IN THE VARIETY GENERATED BY AN IRREDUCIBLE MONO-UNARY ALGEBRA
S. Sukgumpapan and C. Ratanaprasert
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Abstract: Jakubiková Studenovská [4], has described all varieties of mono-unary algebras by identities. In the paper, we characterize all algebras in the variety generated by each irreducible unary algebra and show that for a positive integer nand nonnegative integer k, varieties of the forms and in Jakubiková Studenovská [4] are generated by a cycle and a loop with non-branched tail, respectively. |
Keywords and phrases: unary algebra, cycle, a loop with non-branched tail, irreducible algebra, identities, variety. |
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