Geodesic
Hyperidentities of quasilinear clones containing creative functions
Algebra i logika, Tome 56 (2017) no. 5, pp. 582-592.

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We consider the possibility for separating by hyperidentities clones of quasilinear functions defined on the set $\{0,1,2\}$ with values in the set $\{0,1\}$. It is proved that every creative clone of this kind can be separated by a hyperidentity from any noncreative clone comparable with it.
Keywords: hyperidentity, clone, clone identity, preiterative algebra, separating formula, quasilinear function. 
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I. A. Mal'tsev. Hyperidentities of quasilinear clones containing creative functions. Algebra i logika, Tome 56 (2017) no. 5, pp. 582-592. http://geodesic.mathdoc.fr/item/AL_2017_56_5_a3/

[1] I. A. Maltsev, B. G. Tugylbaeva, “Kongruentsii na podklonakh klona Burle ranga tri, ne soderzhaschikh kreativnykh funktsii”, Sib. matem. zh., 49:5 (2008), 1087–1104 | MR | Zbl

[2] I. A. Maltsev, “Gipertozhdestva kvazilineinykh klonov na trekhelementnom mnozhestve”, Sib. matem. zh., 55:2 (2014), 350–363 | MR | Zbl

[3] W. Taylor, “Hyperidentities and hypervarieties”, Aequationes Math., 23:1 (1981), 30–49 | DOI | MR | Zbl

[4] K. Deneke, I. A. Maltsev, M. Reshke, “O razdelimosti bulevykh klonov gipertozhdestvami”, Sib. matem. zh., 36:5 (1995), 1049–1066 | MR | Zbl

[5] K. Denecke, R. Pöschel, “The characterization of primal algebras by hyperidentities”, General algebra, Dedicated Mem. of Wilfried Nöbauer, Contrib. Gen. Algebra, 6, Hölder-Pichler-Tempsky, Wienna, 1988, 67–87 | MR

[6] M. Reichel, D. Schweigert, D. A. Simovici, “A completeness criterion by functional equations”, Proc. 17th Int. symp. on multiple-valued logic, Boston, 1987, 2–4

[7] I. A. Maltsev, D. Shvaigert, “Gipertozhdestva $QZ$-algebr”, Sib. matem. zh., 30:6 (1989), 132–139 | MR | Zbl

[8] I. A. Maltsev, “O razdelenii klonov kvazilineinykh funktsii gipertozhdestvami”, Materialy konf. Algebra i matematicheskaya logika: teoriya i prilozheniya (g. Kazan, 2–6 iyunya 2014 g.), izd-vo Kazan. un-ta, Kazan, 2014, 101

[9] K. Denecke, S. L. Wismath, Hyperidentities and clones, Algebra, Logic Appl., 14, Gordon and Breach Publ., Amsterdam, 2000 | MR | Zbl

[10] I. A. Maltsev, “Nekotorye svoistva kletok algebr Posta”, Diskret. analiz, 23, 1973, 24–31 | Zbl

[11] Ya. Demetrovich, I. A. Maltsev, “O suschestvenno minimalnykh TC-klonakh na trekhelementnom mnozhestve”, Közl. MTA SZTAKI, 1984, no. 31, 115–151 | MR

[12] Ya. Demetrovich, I. A. Maltsev, “O stroenii klona Burle na trekhelementnom mnozhestve”, Acta Cybernet., 9:1 (1989), 1–25 | MR