The nil radical of power series rings

被引:4
作者
Puczylowski, ER
Smoktunowicz, A
机构
[1] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland
[2] Polish Acad Sci, Inst Math, PL-00950 Warsaw, Poland
关键词
Natural Number; Principal Ideal; Associative Ring; Free Monoid; Nilpotent Ideal;
D O I
10.1007/BF02808186
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We describe the nil radical of power series rings in non-commuting indeterminates by showing that a series belongs to the radical if and only if the ideal generated by its coefficients is nilpotent. We also show that the principal ideals generated by elements of the nil radical of the power series ring in one indeterminate are nil of bounded index.
引用
收藏
页码:317 / 324
页数:8
相关论文
共 11 条
[1]  
Bergman G.M., 1989, ISRAEL MATH C P, V1, P150
[2]  
HAMMAN E, 1986, J ALGEBRA, V100, P260
[3]  
Jacobson Nathan, 1964, American Mathematical Society Colloquium Publications, V37
[4]   THE SUM OF NIL ONE-SIDED IDEALS OF BOUNDED INDEX OF A RING [J].
KLEIN, AA .
ISRAEL JOURNAL OF MATHEMATICS, 1994, 88 (1-3) :25-30
[5]  
KLEIN AA, 1982, CONT MATH, V13, P151
[6]  
Krempa J., 1972, FUND MATH, V76, P121
[7]   PRIME IDEALS IN NORMALIZING EXTENSIONS [J].
PASSMAN, DS .
JOURNAL OF ALGEBRA, 1981, 73 (02) :556-572
[8]   RADICALS OF POLYNOMIAL-RINGS, POWER-SERIES RINGS AND TENSOR-PRODUCTS [J].
PUCZYLOWSKI, ER .
COMMUNICATIONS IN ALGEBRA, 1980, 8 (18) :1699-1709
[9]  
PUCZYLOWSKI ER, 1993, COLLOQ MATH, V61, P209
[10]   NIL IDEALS OF POWER-SERIES RINGS [J].
PUCZYLOWSKI, ER .
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1983, 34 (JUN) :287-292