Abstract
It is well known that the latticeΛ RA of varieties of relation algebras has exactly three atoms. An unsolved problem, posed by B. Jónsson, is to determine the varieties of height two inΛ RA .
This paper solves the corresponding question for varieties generated by total tense algebras. More specifically, we show that there are exactly four finitely generated varieties and infinitely many nonfinitely generated varieties of height two. In the second half of the paper we show that total tense algebras are term equivalent to certain generalized relation algebras and extend our results to varieties of these algebras.
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Jipsen, P., Kramer, R.L. & Maddux, R.D. Total tense algebras and symmetric semiassociative relation algebras. Algebra Universalis 34, 404–423 (1995). https://doi.org/10.1007/BF01182096
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DOI: https://doi.org/10.1007/BF01182096