Geodesic
On local finiteness in varieties of associative algebras
Sbornik. Mathematics, Tome 41 (1982) no. 2, pp. 181-201 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A variety $\mathfrak M$ of algebras is called distinguished if there is a countably generated, locally finite algebra $R\in\mathfrak M$ such that any other countably generated locally finite algebra $A\in\mathfrak M$ is a homomorphic image of $R$. This article continues the investigation of the question of when a variety of associative algebras is distinguished. For example, if the ground field $\Phi$ is uncountable, then every distinguished variety is nonmatric. Note that nonmatric varieties over an algebraically closed field are always distinguished and, over a field $\Phi$ of characteristic zero, a nonmatric variety is distinguished if and only if $\dim_\Phi\widehat\Phi\leqslant\aleph_0$, where $\widehat\Phi$ is the algebraic closure of $\Phi$. Bibliography: 16 titles. 
@article{SM_1982_41_2_a1,
     author = {G. P. Chekanu},
     title = {On local finiteness in varieties of associative algebras},
     journal = {Sbornik. Mathematics},
     pages = {181--201},
     year = {1982},
     volume = {41},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_2_a1/}
}
TY  - JOUR
AU  - G. P. Chekanu
TI  - On local finiteness in varieties of associative algebras
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 181
EP  - 201
VL  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1982_41_2_a1/
LA  - en
ID  - SM_1982_41_2_a1
ER  - 
%0 Journal Article
%A G. P. Chekanu
%T On local finiteness in varieties of associative algebras
%J Sbornik. Mathematics
%D 1982
%P 181-201
%V 41
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1982_41_2_a1/
%G en
%F SM_1982_41_2_a1
G. P. Chekanu. On local finiteness in varieties of associative algebras. Sbornik. Mathematics, Tome 41 (1982) no. 2, pp. 181-201. http://geodesic.mathdoc.fr/item/SM_1982_41_2_a1/

[1] Yu. M. Ryabukhin, “O schetnoporozhdennykh lokalno $\mathfrak M$-algebrakh”, Izv. AN SSSR, seriya matem., 40 (1976), 1203–1223 | Zbl

[2] Yu. M. Ryabukhin, G. P. Chekanu, “O lokalno konechnykh algebrakh”, Teoretiko-koltsevye konstruktsii, vyp. 49, Matem. issledovaniya, izd-vo “Shtiintsa”, Kishinev, 1979, 122–127 | MR

[3] G. P. Chekanu, “Otmechennye mnogoobraziya assotsiativnykh algebr”, Teoretiko-koltsevye konstruktsii, vyp. 49, Matem. issledovaniya, izd-vo “Shtiintsa”, Kishinev, 1979, 149–158 | MR

[4] S. Leng, Algebra, izd-vo “Mir”, Moskva, 1968

[5] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Koltsa, blizkie k assotsiativnym, izd-vo “Nauka”, Moskva, 1978 | MR

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

[7] A. I. Maltsev, “O razlozhenii algebry v pryamuyu summu radikala i poluprostoi podalgebry”, DAN SSSR, 36:2 (1942), 46–50

[8] V. M. Kurochkin, “Rasscheplenie algebr v polupryamuyu summu radikala i poluprostoi podalgebry”, Uchenye zapiski MGU, 148 (1951), 192–203 | MR

[9] E. N. Zakharova, “O radikalno-poluprostykh klassakh i silnoi $J$-poluprostote lokalno konechnykh $PI$-algebr”, Teoretiko-koltsevye konstruktsii, vyp. 49, Matem. issledovaniya, izd-vo “Shtiintsa”, Kishinev, 1979, 68–79 | MR

[10] V. N. Latyshev, “Obobschenie teoremy Gilberta o konechnosti bazisov”, Sib. matem. zh., 7:6 (1966), 1422–1424 | Zbl

[11] V. N. Latyshev, “O slozhnosti nematrichnykh mnogoobrazii”, Algebra i logika, 16:2 (1977), 149–183 | MR | Zbl

[12] Yu. M. Ryabukhin, G. P. Chekanu, “O lokalno konechnykh algebrakh”, III Vsesoyuznyi simpozium po teorii kolets modulei i algebr, tezisy soobschenii, 87, Tartu, 1976

[13] N. Kherstein, Nekommutativnye koltsa, izd-vo “Mir”, Moskva, 1972 | MR

[14] A. I. Maltsev, Algebraicheskie sistemy, izd-vo “Nauka”, Moskva, 1970 | MR

[15] N. Burbaki, Algebra. Mnogochleny i polya, uporyadochennye gruppy, izd-vo “Nauka”, Moskva, 1965 | MR

[16] B. L. Van-der Varden, Algebra, izd-vo “Nauka”, Moskva, 1976 | MR