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

来源：

ISRAEL JOURNAL OF MATHEMATICS | 1999年 / 110卷 / 1期

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

页码：317 / 324

页数：8

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].