Geodesic
Cross varieties of algebras
Sbornik. Mathematics, Tome 43 (1982) no. 3, pp. 347-376 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper gives sufficient conditions and a method for establishing that a variety generated by a finite algebra is Cross. As a corollary, it is established that the varieties generated by finite alternative, Jordan, Mal'tsev, and $(\gamma,\delta)$-algebras are Cross. Bibliography: 14 titles. 
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     author = {Yu. A. Medvedev},
     title = {Cross varieties of algebras},
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Yu. A. Medvedev. Cross varieties of algebras. Sbornik. Mathematics, Tome 43 (1982) no. 3, pp. 347-376. http://geodesic.mathdoc.fr/item/SM_1982_43_3_a4/

[1] Vakhturin Yu. A., Olshanskii A. Yu., “Tozhdestvennye sootnosheniya v konechnykh koltsakh Li”, Matem. sb., 96(132) (1975), 543–559

[2] Zhevlakov K. A., Shestakov I. P., “O lokalnoi konechnosti v smysle Shirshova”, Algebra i logika, 12:1 (1973), 41–73

[3] Lvov I. V., “O mnogoobraziyakh assotsiativnykh kolets. I”, Algebra i logika, 12:3 (1973), 269–297 | MR

[4] Lvov I. V., “O mnogoobraziyakh, porozhdennykh konechnymi alternativnymi koltsami”, Algebra i logika, 17:3 (1978), 282–286 | MR

[5] Lvov I. V., “Konechnomernye algebry s beskonechnymi bazisami tozhdestv”, Sib. matem. zh., 19:1 (1978), 91–99 | MR

[6] Medvedev Yu. A., “Tozhdestva konechnykh iordanovykh $P$-algebr”, Algebra i logika, 18:6 (1979), 723–748 | MR | Zbl

[7] Neiman X., Mnogoobraziya grupp, Mir, M., 1969 | MR

[8] Nikitin A. A., “Pochti alternativnye algebry”, Algebra i logika, 13:5 (1974), 501–533 | MR | Zbl

[9] Polin S. V., “O tozhdestvakh konechnykh algebr”, Sib. matem. zh., 17:6 (1976), 1356–1366 | MR | Zbl

[10] Jacobson N., Structure and representations of Jordan algebra's, Amer. Math. Soc., Providence: R. I., 1968 | MR | Zbl

[11] Kruse R. L., “Identities satisfied by a finite rings”, J. Algebra, 26 (1973), 298–318 | DOI | MR | Zbl

[12] Oates S., Powell M. B., “Identical relations in finite groups”, J. Algebra, 1 (1964), 11–39 | DOI | MR | Zbl

[13] Towers D. A., “A Frattini theory for algebras”, Proc. London Math. Soc., 17:3 (1973), 440–462 | DOI | MR

[14] Pchelintsev S. V., “Nilpotentnost assotsiatornogo ideala svobodnogo konechnoporozhdennogo $(-1,1)$-koltsa”, Algebra i logika, 14:5 (1975), 543–571 | MR | Zbl