Geodesic
Algebraic automorphisms and $PI$-algebras
Sbornik. Mathematics, Tome 26 (1975) no. 1, pp. 55-69 
V. E. Barbaumov. Algebraic automorphisms and $PI$-algebras. Sbornik. Mathematics, Tome 26 (1975) no. 1, pp. 55-69. http://geodesic.mathdoc.fr/item/SM_1975_26_1_a2/
@article{SM_1975_26_1_a2,
     author = {V. E. Barbaumov},
     title = {Algebraic automorphisms and $PI$-algebras},
     journal = {Sbornik. Mathematics},
     pages = {55--69},
     year = {1975},
     volume = {26},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_26_1_a2/}
}
TY  - JOUR
AU  - V. E. Barbaumov
TI  - Algebraic automorphisms and $PI$-algebras
JO  - Sbornik. Mathematics
PY  - 1975
SP  - 55
EP  - 69
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1975_26_1_a2/
LA  - en
ID  - SM_1975_26_1_a2
ER  - 
%0 Journal Article
%A V. E. Barbaumov
%T Algebraic automorphisms and $PI$-algebras
%J Sbornik. Mathematics
%D 1975
%P 55-69
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1975_26_1_a2/
%G en
%F SM_1975_26_1_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is concerned with associative algebras over a field of characteristic zero which possess a $d$-regular algebraic automorphism. (An automorphism is called $d$-regular if the subalgebra of fixed elements satisfies an identity of degree $d$.) It is shown that if an algebra admits a $d$-regular algebraic automorphism such that no root of unity is a multiple root of its minimum polynomial, then it is a $PI$-algebra. Bibliography: 8 titles.

[1] E. M. Patterson, “On regular automorphisms of certain classes of rings”, Quart. J. Math., 12:46 (1961), 127–133 | DOI | MR | Zbl

[2] S. A. Amitsur, “Rings with involution”, Israel. J. Math., 6 (1968), 99–106 | DOI | MR | Zbl

[3] V. E. Barbaumov, “Avtomorfizmy i $PI$-algebry”, Uspekhi matem. nauk, XXVIII:1 (169) (1973), 231–232 | MR

[4] V. E. Barbaumov, “Gruppy avtomorfizmov i $PI$-algebry”, Sib. matem. zh., XV (1975)

[5] G. M. Bergman, I. M. Isaacs, “Rings with fixed-point-free group actions”, Proc. London Math. Soc. (3), 27 (1973), 69–87 | DOI | MR | Zbl

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

[7] S. Wallace, W. S. Martindale, “Rings with involution and polynomial identities”, J. algebra, 11 (1969), 186–194 | DOI | MR

[8] N. Dzhekobson, Stroenie kolets, IL, Moskva, 1961