A simple solution of the ADS-problem

被引:0
作者
Andruszkiewicz, Ryszard R. [1 ]
Hryniewicka, Malgorzata E. [1 ]
Pryszczepko, Karol [1 ]
机构
[1] Univ Bialystok, Inst Math, Ciolkowskiego 1M, PL-15245 Bialystok, Poland
关键词
Ideals; accessible rings; lower radical; Kurosh chain;
D O I
10.2989/16073606.2019.1572665
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The main aim of this note is to give a new and elementary proof of the Beidar theorem, which asserts that for every positive integer n there exists a homomorphically closed class of rings with the Kurosh chain terminating precisely at the n-th step.
引用
收藏
页码:243 / 250
页数:8
相关论文
共 19 条
[1]  
Amitsur S.A., 1954, AM J MATH, V76, P126, DOI DOI 10.2307/2372404
[2]  
Amitsur SA., 1954, Am. J. Math, V76, P100, DOI DOI 10.2307/2372403
[3]  
Amitsur SA., 1952, Amer. J. Math., V74, P774
[4]   ACCESSIBLE SUBRINGS AND KUROSH'S CHAINS OF ASSOCIATIVE RINGS [J].
Andruszkiewicz, Ryszard R. ;
Sobolewska, Magdalena .
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2013, 95 (02) :145-157
[5]  
BEIDAR KI, 1982, CZECH MATH J, V32, P418
[6]   SKEW DERIVATIONS AND THE NIL AND PRIME RADICALS [J].
Bergen, Jeffrey ;
Grzeszczuk, Piotr .
COLLOQUIUM MATHEMATICUM, 2012, 128 (02) :229-236
[7]   Jacobson radicals of ring extensions [J].
Bergen, Jeffrey ;
Grzeszczuk, Piotr .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2012, 216 (12) :2601-2607
[8]  
Filippov V.T., 2006, Non-associative algebra and its applications, V246, P461
[9]   On the nil radical [J].
France-Jackson, H. .
ACTA MATHEMATICA HUNGARICA, 2015, 146 (01) :220-223
[10]  
Gardner BJ, 2007, ALGEBRA DISCRET MATH, P15