Theorems on equalization and monomiality in a~relatively free Grassmann algebra
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 197-218.

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In this paper, we prove theorems on equalization and monomiality, which are essential for developing the structural theory of T-spaces in a relatively free algebra $k\langle1,x_1,\dots,x_i,\dots\rangle/([[x_1,x_2],x_3])^T$ over an infinite field $k$ of characteristic $p>2$. Additionally, some specifics of the case $p=2$ are considered.
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L. M. Tsybulya. Theorems on equalization and monomiality in a~relatively free Grassmann algebra. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 197-218. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a14/

[1] Belov A. Ya., “O neshpekhtovykh mnogoobraziyakh”, Fundament. i prikl. mat., 5:1 (1999), 47–66 | MR | Zbl

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

[3] Grishin A. V., “O konechnoi baziruemosti abstraktnykh T-prostranstv”, Fundament. i prikl. mat., 1:3 (1995), 669–700 | MR | Zbl

[4] Grishin A. V., “Primery ne konechnoi baziruemosti T-prostranstv i T-idealov v kharakteristike 2”, Fundament. i prikl. mat., 5:1 (1999), 101–118 | MR | Zbl

[5] Grishin A. V., Surmina L. M., “O T-algebre $n$-slov”, Mezhdunar. konf. po algebre i teorii chisel, posvyaschennaya 80-letiyu V. E. Voskresenskogo, Tezisy dokladov (Samara, 21–25 maya 2007 g.), 15–16

[6] Grishin A. V., Surmina L. M., “O T-prostranstvakh $n$-slov nad polem kharakteristiki $p>0$”, Uspekhi mat. nauk, 62:4 (2007), 145–146 | MR | Zbl

[7] Grishin A. V., Urbakhanov S. V., “O korazmernostyakh v prostranstvakh 2-slov nad polem kharakteristiki 2 i svoistvakh ekstremalnosti”, Chebyshevskii sb., 3:2 (2002), 34–42 | MR | Zbl

[8] Grishin A. V., Tsybulya L. M., “O $(p,n)$-probleme”, Vestn. SamGU. Estestvennonauch. ser. Mat., 57:7 (2007), 35–55

[9] Grishin A. V., Tsybulya L. M., “Dve teoremy o stroenii otnositelno svobodnoi algebry Grassmana”, Uspekhi mat. nauk, 63:4 (2008), 186–187 | MR

[10] Chiripov P. Zh., Siderov P. N., “O bazisakh tozhdestv nekotorykh mnogoobrazii assotsiativnykh algebr”, Pliska, 1981, no. 2, 103–115 | MR | Zbl

[11] Schigolev V. V., “Konechnaya baziruemost T-prostranstv nad polyami nulevoi kharakteristiki”, Izv. RAN. Ser. mat., 65:5 (2001), 191–224 | MR | Zbl

[12] Schigolev V. V., “Primery beskonechno baziruemykh T-idealov”, Fundament. i prikl. mat., 5:1 (1999), 307–312 | MR | Zbl

[13] Grishin A. V., Shchigolev V. V., “On T-spaces and their applications”, J. Math. Sci., 134:1 (2006), 1799–1878 | DOI | MR | Zbl

[14] Gupta C. K., Krasilnikov A. N., “A non-finitely based system of polinomial identities which contains the identity $x^6=0$”, Quart. J. Math., 53 (2002), 173–183 | DOI | MR | Zbl

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