环的(k,l,m,n)一根

The (k,l, m,n) -radical of rings

中文摘要:

      

英文摘要:

      The concept of the (k,l,m,n) - radical was sintroduced by Szasz in[ 2 ]. In this paper, it is proved that the (k,l,m,n) -radical is a radical in the sense of Amitsur and Kurosh . and the structure of the (k,l,m,n) radical is given with the met hod of constructing upper radicals, for every quadruple of non- negative integers, k,l,m,n .As a corollary of the theorem in this paper, Szasz's results in [3] are imme-diately derived.It is also proved that the (k,l,m,n) radical of the full matrix ring over a ring A.