Geodesic
Some estimates for the least power of identities of subspaces $M_1^{(m,k)}(F)$ of the matrix superalgebra $M^{(m,k)}(F)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 13-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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We estimate the least power of identities of subspaces $M_1^{(m, k)}(F)$ of the matrix superalgebra $M^{(m, k)}(F)$ over the field $F$ for any $m$ and $k$. For subspaces $M_1^{(m, 1)}(F)$ $(m\geq1)$ and $M_1^{(2,2)}(F)$ we obtain concrete minimal identities.
Keywords: $T$-ideal, polynomial identity, matrix superalgebra. 
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     title = {Some estimates for the least power of identities of subspaces $M_1^{(m,k)}(F)$ of the matrix superalgebra $M^{(m,k)}(F)$},
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S. Yu. Antonov. Some estimates for the least power of identities of subspaces $M_1^{(m,k)}(F)$ of the matrix superalgebra $M^{(m,k)}(F)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 13-27. http://geodesic.mathdoc.fr/item/IVM_2012_5_a1/

[1] Dnestrovskaya tetrad: Nereshennye problemy teorii kolets i modulei, izd. 2, In-t matematiki SO AN SSSR, Novosibirsk, 1976

[2] Kemer A. R., Ideals of identities of associative algebras, Translation of Mathematical Monographs, 87, Amer. Math. Soc., Providence, RI, 1991 | MR | Zbl

[3] Amitsur S. A., Levitzki J., “Minimal identities for algebras”, Proc. Amer. Math. Soc., 1:4 (1950), 449–463 | DOI | MR | Zbl

[4] Averyanov I. V., “Bazis graduirovannykh tozhdestv superalgebry $M_{1,2}(F)$”, Matem. zametki, 85:4 (2009), 483–501 | MR | Zbl

[5] Antonov S. Yu., “Naimenshaya stepen graduirovannykh tozhdestv matrichnoi superalgebry $M_3(F)$”, Tr. XVIII mezhd. letnei shkoly-sem. “Volga 18' 06”, 2006, 17–22

[6] Antonov S. Yu., “Naimenshaya stepen tozhdestv podprostranstva $M_1^{(2,1)}(F)$ matrichnoi superalgebry $M^{(2,1)}(F)$”, Tr. mezhd. konferentsii KLIN-2007, v. 4, UlGTU, Ulyanovsk, 2007, 27–30

[7] Domokos M., “A generalization of a theorem of Chang”, Comm. Algebra, 23:12 (1995), 4333–4342 | DOI | MR | Zbl