Geodesic
On Some Extremal Varieties of Associative Algebras
Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 542-558.

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Suppose that $F$ is a field of prime characteristic $p$ and $\mathbf V_p$ is the variety of associative algebras over $F$ defined by the identities $[[x,y],z]=0$ and $x^p=0$ if $p>2$ and by the identities $[[x,y],z]=0$ and $x^4=0$ if $p=2$ (here $[x,y]=xy-yx$). As is known, the free algebras of countable rank of the varieties $\mathbf V_p$ contain non-finitely generated $T$-spaces. We prove that the varieties $\mathbf V_p$ are minimal with respect to this property. 
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E. A. Kireeva; A. N. Krasilnikov. On Some Extremal Varieties of Associative Algebras. Matematičeskie zametki, Tome 78 (2005) no. 4, pp. 542-558. http://geodesic.mathdoc.fr/item/MZM_2005_78_4_a5/

[1] Bakhturin Yu. A., Olshanskii A. Yu., “Tozhdestva”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 18, VINITI, M., 1988, 117–240

[2] Bokut L. A., Lvov I. V., Kharchenko V. K., “Nekommutativnye koltsa”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 18, VINITI, M., 1988, 5–116

[3] Drensky V. S., Free Algebras and PI-Algebras. Graduate Course in Algebra, Springer-Verlag Singapore, Singapore, 2000 | MR

[4] Rowen L. H., Ring Theory, Academic Press, Boston, 1991 | MR | Zbl

[5] Specht W., “Gesetze in Ringen”, Math. Z., 52 (1950), 557–589 | DOI | MR | Zbl

[6] Kemer A. R., “Mnogoobraziya $\mathbb Z_2$-graduirovannye algebry”, Izv. AN SSSR. Ser. matem., 48:5 (1984), 1042–1059 | MR

[7] Kemer A. R., “Konechnaya baziruemost tozhdestv assotsiativnykh algebr”, Algebra i logika, 26 (1987), 597–641

[8] Belov A. Ya., “O neshpekhtovykh mnogoobraziyakh”, Fundament. i prikl. matem., 5 (1999), 47–66 | Zbl

[9] Grishin A. V., “Primery ne konechnoi baziruemosti $T$-prostranstv i $T$-idealov v kharakteristike $2$”, Fundament. i prikl. matem., 5 (1999), 101–118 | Zbl

[10] Schigolev V. V., “Primery beskonechno baziruemykh $T$-idealov”, Fundament. i prikl. matem., 5 (1999), 307–312 | Zbl

[11] Belov A. Ya., “Kontrprimery k probleme Shpekhta”, Matem. sb., 191:3 (2000), 13–24 | Zbl

[12] Grishin A. V., “On non-Spechtianness of the variety of associative rings that satisfy the identity $x^{32}=0$”, Electronic Research Announcements of the Amer. Math. Soc., 2000, no. 6, 50–51 | DOI | Zbl

[13] Grishin A. V., “O konechnoi baziruemosti sistem obobschennykh mnogochlenov”, Izv. AN SSSR. Ser. matem., 54:5 (1990), 899–927 | Zbl

[14] Chiripov P. Zh., Siderov P. N., “O bazisakh tozhdestv nekotorykh mnogoobrazii assotsiativnykh algebr”, Pliska, 2 (1981), 103–115 | Zbl

[15] Schigolev V. V., “Primery beskonechno baziruemykh $T$-prostranstv”, Matem. sb., 191:3 (2000), 143–160 | MR | Zbl

[16] Latyshev V. N., “O vybore bazy v odnom $T$-ideale”, Sib. matem. zh., 4:5 (1963), 1122–1126

[17] Krasilnikov A. N., “O tozhdestvakh trianguliruemykh matrichnykh predstavlenii grupp”, Tr. MMO, 52, URSS, M., 1989, 229–245

[18] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985