Geodesic
On Commutative Unary Algebras with Totally Ordered Congruence Lattice
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 80-92

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The class of all commutative unary algebras (with arbitrarily many operations) with totally ordered congruence lattice is described.
Keywords: commutative unary algebra, totally ordered congruence lattice, unar, reduct, characteristic semigroup. 
A. V. Kartashova. On Commutative Unary Algebras with Totally Ordered Congruence Lattice. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 80-92. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a6/
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[1] J. Berman, “On the congruence lattices of unary algebras”, Proc. Amer. Math. Soc., 36:1 (1972), 34–38 | DOI | MR | Zbl

[2] D. P. Egorova, L. A. Skornyakov, “O strukture kongruentsii unarnoi algebry”, Uporyadochennye mnozhestva i reshetki, 4, Mezhvuz. nauch. sb., Izd-vo Saratovsk. un-ta, Saratov, 1977, 28–40 | MR | Zbl

[3] D. P. Egorova, “Struktura kongruentsii unarnoi algebry”, Uporyadochennye mnozhestva i reshetki, 5, Mezhvuz. nauch. sb., Izd-vo Saratovsk. un-ta, Saratov, 1978, 11–44 | MR | Zbl

[4] G. Grätzer, E. T. Schmidt, “Characterizations of congruence lattices of abstract algebras”, Acta Sci. Math. (Szeged), 24 (1963), 34–59 | MR | Zbl

[5] J. Johnson, R. L. Seifert, A Survey of Multi-Unary Algebras, Mimeographed seminar notes, University of California, Berkeley, CA, 1967

[6] Z. Ésik, B. Imreh, “Subdirectly irreducible commutative automata”, Acta Cybernet., 5:3 (1981), 251–260 | MR | Zbl

[7] A. V. Kartashova, “O kommutativnykh unarnykh algebrakh s lineino uporyadochennoi reshetkoi kongruentsii”, Algebra i matematicheskaya logika, Kazanskii (Privolzhskii) federalnyi un-t, Kazan, 2011, 104–106

[8] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[9] Z. Ésik, B. Imreh, “Remarks on finite commutative automata”, Acta Cybernet., 5:3 (1981), 143–146 | MR | Zbl

[10] S. Bogdanović, M. Ćirić, T. Petrović, B. Imreh, M. Steinby, “Traps, cores, extensions and subdirect decompositions of unary algebras”, Fund. Inform., 38:1-2 (1999), 51–60 | MR | Zbl

[11] L. Fuchs, Abelian Groups, Publ. House of the Hungar. Acad. of Sci., Budapest, 1958 | MR

[12] V. K. Kartashov, “Nezavisimye sistemy porozhdayuschikh i svoistvo Khopfa dlya unarnykh algebr”, Diskret. matem., 20:4 (2008), 79–84 | DOI | MR | Zbl

[13] A. V. Kartashova, “O konechnykh reshetkakh topologii kommutativnykh unarnykh algebr”, Diskret. matem., 21:3 (2009), 119–131 | DOI | MR