Geodesic
Basic $\mathbb{T}$-spaces in the relatively free Grassmann algebra without unity
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 209-224.

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In this paper, we consider the $\mathbb{T}$-space structure of the relatively free Grassmann algebra $\mathbb{F}^{(3)}$ without unity over an infinite field of prime and zero characteristic. Our work is focused on $\mathbb{T}$-spaces $\mathbb{W}_n$ generated by all $n$-words. A question about connections between $\mathbb{W}_r$ and $\mathbb{W}_n$ for different natural numbers $r$ and $n$ is investigated. The proved theorem on these connections allows us to construct the diagrams of inclusions that, to some extent, clarify the structure of the algebra: the basic $\mathbb{T}$-spaces produce infinite strictly descending chains of inclusions in the algebra $\mathbb{F}^{(3)}$. 
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L. M. Tsybulya. Basic $\mathbb{T}$-spaces in the relatively free Grassmann algebra without unity. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 209-224. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a11/

[1] Aladova E. V., Grishin A. V., Kireeva E. A., “$T$-prostranstva. Istoriya voprosa, prilozheniya i poslednie rezultaty”, Chebyshevskii sb., 5:4(112) (2004), 39–57 | MR | Zbl

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

[3] Grishin A. V., “O konechnoi baziruemosti abstraktnykh $T$-prostranstv”, Fundament. i prikl. matem., 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. matem., 5:1 (1999), 101–118 | MR | Zbl

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

[6] Grishin A. V., Tsybulya L. M., “O $T$-prostranstvennom i multiplikativnom stroenii otnositelno svobodnoi algebry Grassmana”, Matem. sb., 200:9 (2009), 41–80 | MR | Zbl

[7] Grishin A. V., Tsybulya L. M., “O strukture otnositelno svobodnoi algebry Grassmana”, Fundament. i prikl. matem., 15:8 (2009), 3–93

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

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

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