Geodesic
The Property of Having Independent Basis in Semigroup Varieties
Algebra i logika, Tome 44 (2005) no. 1, pp. 81-96.

Voir la notice de l'article provenant de la source Math-Net.Ru

There exist independently based semigroup varieties $\mathfrak X$ and $\mathfrak Y$, $\mathfrak X\subset \mathfrak Y$, such that $\mathfrak X$ has no cover in the interval $[\mathfrak X; \mathfrak Y]$.
Keywords: semigroup variety, independently based variety. 
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V. Yu. Popov. The Property of Having Independent Basis in Semigroup Varieties. Algebra i logika, Tome 44 (2005) no. 1, pp. 81-96. http://geodesic.mathdoc.fr/item/AL_2005_44_1_a5/

[1] I. Reznikoff, “Tout ensemble de formules de la logique classique est equivalent a un ensemble independant”, C. R. Acad. Sci. Paris, 260 (1965), 2385–2388 | MR | Zbl

[2] A. Tarski, “Equational logic and equational theories of algebras”, Contrib. Math. Logic, Proc. Logic Colloq. (Hannover, 1966), North-Holland, Amsterdam, 1968, 275–288 | MR | Zbl

[3] A. I. Maltsev, “Universalno aksiomatiziruemye podklassy lokalno konechnykh klassov modelei”, Sib. matem. zh., 8:5 (1967), 1005–1014

[4] V. A. Gorbunov, Algebraicheskaya teoriya kvazimnogoobrazii, Sibirskaya shkola algebry i logiki, Nauchnaya kniga (NII MIOO NGU), Novosibirsk, 1999 | Zbl

[5] L. N. Shevrin, M. V. Volkov, “Tozhdestva polugrupp”, Izv. vuzov, Matematika, 1985, no. 11, 3–47 | MR | Zbl

[6] A. N. Trakhtman, “Mnogoobrazie polugrupp bez neprivodimogo bazisa tozhdestv”, Matem. zametki, 21:6 (1977), 865–872 | MR | Zbl

[7] G. Pollak, “Some lattices of varieties containing elements without cover”, Quad. Ric. Sci., 109 (1981), 91–96 | MR | Zbl

[8] M. V. Sapir, “142–143”, 16-ya Vsesoyuzn. algebr. konf., ch. 2, Leningrad, 1981

[9] A. N. Trakhtman, “Shestielementnaya polugruppa, porozhdayuschaya mnogoobrazie s kontinuumom podmnogoobrazii”, Algebraicheskie sistemy i ikh mnogoobraziya, Sverdlovsk, 1988, 138–143 | MR | Zbl

[10] E. I. Kleiman, “Ob uslovii pokrytiya v reshëtke mnogoobrazii inversnykh polugrupp”, Issledovanie algebraicheskikh sistem po svoistvam ikh podsistem, Sverdlovsk, 1980, 76–91 | MR | Zbl

[11] Yu. G. Kleiman, “O nekotorykh voprosakh teorii mnogoobrazii grupp”, Izv. AN SSSR, Ser. matem., 47:1 (1983), 37–74 | MR | Zbl

[12] Sverdlovskaya tetrad. Nereshënnye zadachi teorii polugrupp, Sverdlovsk, 1979

[13] P. Perkins, Decision problems for equational theories of semigroups and general algebras, Ph. D. th., Univ. California, Berkeley, Calif., 1966

[14] D. R. Bean, A. Ehrenfeucht, G. McNulty, “Avoidable patterns in strings of symbols”, Pac. J. Math., 85:2 (1972), 261–294 | MR

[15] A. I. Zimin, “Blokiruyuschie mnozhestva termov”, Matem. sb., 119:3 (1982), 363–375 | MR

[16] P. Perkins, “Bases for equational theories of semigroups”, J. Algebra, 11:2 (1969), 298–314 | DOI | MR | Zbl

[17] V. A. Gorbunov, “Pokrytiya v reshëtkakh kvazimnogoobrazii i nezavisimaya aksiomatiziruemost”, Algebra i logika, 16:5 (1977), 507–548 | MR | Zbl