| Prof. Edmund R. Puczylowski
(
University of Warsaw, Poland )
On The Structure of Ring Which are Sums of Two Subrings
摘要
| | Let R be a ring and R_1, R_2 its subrings such that R=R_1+R_2, i.e., for every element r \in R there are r_1 and r_2 such that r=r_1+r_2.
Results of many papers show that relations between properties of R and those of the subrings are quite unclear. It is for instance unknown whether if R_1 is nilpotent and R_2 is nil, then R is nil. This question is actually equivalent to the famous Koethe's problem. It in particular means that a description of the nil radical of rings which are sums of two subrings is a hopeless problem. In the talk we shall discuss when the nil radical is equal to one of the subrings, say R_1. It seems to be possible that it is so when R_1 is nil and R_2 is reduced. We shall show that this is indeed true in a number of cases. This is my joint work with M. Kepczyk.
|
90年4月26日 (星期四)
14:10-15:00
台灣大學數學系新數館308室
|