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 Mat. Sb. (N.S.), 1983, Volume 122(164), Number 1(9), Pages 31–40 (Mi msb2271)

This article is cited in 17 scientific papers (total in 17 papers)

Finitely generated special Jordan and alternative $PI$-algebras

I. P. Shestakov

Abstract: The author explores the question of whether identities related to special Jordan and alternative $PI$-algebras exist in associative algebras. It is proved that if $A$ is a finitely generated special Jordan (alternative) $PI$-algebra, then the universal associative enveloping algebra $S(A)$ (respectively, the universal algebra $\mathscr R(A)$ for right alternative representations) of algebra $A$ is also a $PI$-algebra. As a corollary it is proved that the upper nilradical of a finitely generated special Jordan or alternative $PI$-algebra over a Noetherian ring is nilpotent. A similar result holds for the Zhevlakov radical of a finitely generated free alternative algebra. In addition, a criterion is obtained for local associator nilpotence of an alternative algebra.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 50:1, 31–40

Bibliographic databases:

UDC: 519.48
MSC: Primary 17C25; Secondary 17C10, 16A68
Received: 18.06.1982

Citation: I. P. Shestakov, “Finitely generated special Jordan and alternative $PI$-algebras”, Mat. Sb. (N.S.), 122(164):1(9) (1983), 31–40; Math. USSR-Sb., 50:1 (1985), 31–40

Citation in format AMSBIB
\Bibitem{She83} \by I.~P.~Shestakov \paper Finitely generated special Jordan and alternative $PI$-algebras \jour Mat. Sb. (N.S.) \yr 1983 \vol 122(164) \issue 1(9) \pages 31--40 \mathnet{http://mi.mathnet.ru/msb2271} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=715833} \zmath{https://zbmath.org/?q=an:0549.17013|0524.17008} \transl \jour Math. USSR-Sb. \yr 1985 \vol 50 \issue 1 \pages 31--40 \crossref{https://doi.org/10.1070/SM1985v050n01ABEH002731} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Pchelintsev, “A theorem on height for alternative algebras”, Math. USSR-Sb., 52:2 (1985), 541–551
2. S. V. Pchelintsev, “Prime algebras and absolute zero divisors”, Math. USSR-Izv., 28:1 (1987), 79–98
3. Yu. A. Medvedev, “Representations of finitely generated Jordan PI-algebras”, Math. USSR-Izv., 32:1 (1989), 63–76
4. A. Ya. Belov, “On a Shirshov basis of relatively free algebras of complexity $n$”, Math. USSR-Sb., 63:2 (1989), 363–374
5. E. I. Zel'manov, I. P. Shestakov, “Prime alternative superalgebras and the nilpotence of the radical of a free alternative algebra”, Math. USSR-Izv., 37:1 (1991), 19–36
6. V. T. Markov, “On matrix algebras with two generators and on embedding $PI$-algebras”, Russian Math. Surveys, 47:4 (1992), 216–217
7. Plamen Koshlukov, “Polynomial identities for Jordan pairs”, Communications in Algebra, 22:8 (1994), 2749
8. M. M. Babikov, “A criterion for the solvability of alternative algebras”, Math. Notes, 57:3 (1995), 229–234
9. José A. Anquela, Teresa Cortés, Fernando Montaner, “The structure of primitive quadratic Jordan algebras”, Journal of Algebra, 172:2 (1995), 530
10. S. V. Pchelintsev, “Nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra”, Siberian Math. J., 45:2 (2004), 356–375
11. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260
12. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267
13. Shestakov I., Zhukavets N., “The Free Alternative Superalgebra on One Odd Generator”, Int. J. Algebr. Comput., 17:5-6 (2007), 1215–1247
14. Zhukavets N.M., Shestakov I.P., “A Base of the Free Alternative Superalgebra on One Odd Generator”, Dokl. Math., 78:2 (2008), 693–695
15. Shestakov I.P., Kornev A.I., “On the Radical of a Free Malcev Algebra”, Proc. Amer. Math. Soc., 140:9 (2012), 3049–3054
16. KanelBelov A. Karasik Y. Rowen L., “Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition”, Computational Aspects of Polynomial Identities: Vol 1, Kemer'S Theorems, 2Nd Edition, Monographs and Research Notes in Mathematics, 16, Crc Press-Taylor & Francis Group, 2016, 1–407
17. Pchelintsev S.V., “Proper identities of finitely generated commutative alternative algebras”, J. Algebra, 470 (2017), 425–440
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