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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2025, Number 3, Pages 17–24
DOI: https://doi.org/10.26907/0021-3446-2025-3-17-24 (Mi ivm10070) 		 
On the structure of $\mathrm T$-spaces of free associative Grassmann algebra of rank $2$

V. I. Glizburga, S. V. Pchelintsevb

a Moscow City Pedagogical University, 4 Sel'skohozyaistvennyi drive, Moscow, 129226 Russia
b Financial University under the Government of the Russian Federation, 49 Leningradskii Ave., Moscow, 125993 Russia
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DOI: https://doi.org/10.26907/0021-3446-2025-3-17-24
Abstract: We study $\mathrm T$-spaces contained in free associative Grassmann algebra $F_2^{(3)}$ of rank $2$ over an infinite field of finite characteristic. Systems of generators of these $\mathrm T$-spaces are found. It is proved that the $\mathrm T$-spaces contained in the commutant form a chain.
Keywords: free associative Grassmann algebra, commutant, center, $\mathrm T$-space.
Received: 11.03.2024
Revised: 25.04.2024
Accepted: 26.06.2024
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2025, Volume 69, Issue 3, Pages 12–18
DOI: https://doi.org/10.3103/S1066369X25700203
Document Type: Article
UDC: 512.554
Language: Russian
Citation: V. I. Glizburg, S. V. Pchelintsev, “On the structure of $\mathrm T$-spaces of free associative Grassmann algebra of rank $2$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2025, no. 3, 17–24; Russian Math. (Iz. VUZ), 69:3 (2025), 12–18
Citation in format AMSBIB
\Bibitem{GliPch25}
\by V.~I.~Glizburg, S.~V.~Pchelintsev
\paper On the structure of $\mathrm T$-spaces of free associative Grassmann algebra of rank $2$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2025
\issue 3
\pages 17--24
\mathnet{http://mi.mathnet.ru/ivm10070}
\crossref{https://doi.org/10.26907/0021-3446-2025-3-17-24}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2025
\vol 69
\issue 3
\pages 12--18
\crossref{https://doi.org/10.3103/S1066369X25700203}
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