Abstract
We are particularly interested in the proper subvarieties of \(\mathcal{N}\) and \(\mathcal{N}^{0}\) that are determined by the equation \(f^{r}x \approx f^{s}x\) for some pair r < s. Thus, for 0 ≤ r < s, we consider the following varieties.
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Bibliography
K. Adaricheva, J.B. Nation, Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Parts I and II. Int. J. Algebra Comput. 22, N7 (2012)
A. Basheyeva, A. Nurakunov, M. Schwidefsky, A. Zamojska-Dzienio, Lattices of subclasses, III. Siberian Elektron. Mat. Izv. 14, 252–263 (2017)
V.A. Gorbunov, Algebraic Theory of Quasivarieties (Plenum, New York, 1998)
J. Hyndman, R. McKenzie, W. Taylor, k-ary monoids of term operations. Semigroup Forum 44, 21–52 (1992)
V.K. Kartashov, Quasivarieties of unars. Matemasticheskie Zametki 27, 7–20 (1980, in Russian); English translation in Math. Notes 27 (1980), 5–12
V.K. Kartashov, Quasivarieties of unars with a finite number of cycles. Algebra Logika 19, 173–193, 250 (1980, in Russian); English translation in Algebra Logic 19, 106–120 (1980)
V.K. Kartashov, Lattices of quasivarieties of unars. Sibirsk. Mat. Zh. 26, 49–62, 223 (1985, in Russian); English translation in Siberian Math. J. 26 (1985), 346–357
V.K. Kartashov, Characterization of the lattice of quasivarieties of the algebras \(\mathfrak{A}_{1,1}\), in Algebraic Systems (Volgograd. Gos. Ped. Inst., Volgograd, 1989, in Russian), pp. 37–45
V.K. Kartashov, S.P. Makaronov, Quasivarieties of unars with zero, in Algebraic Systems (Volgograd. Gos. Ped. Inst., Volgograd, 1989, in Russian), pp. 139–143
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Hyndman, J., Nation, J.B. (2018). 1-Unary Algebras. In: The Lattice of Subquasivarieties of a Locally Finite Quasivariety. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-78235-5_6
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DOI: https://doi.org/10.1007/978-3-319-78235-5_6
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