环的(k,l,m,n)一根

Brown和McCoy在文1]中建立了(F,Ω)-群的根理论,并由此考察了环的BrownMcCoy-根及其它一些根,根据这一方法,Szsz在文2]中引进了环的(k,l,m,n)-根,其中k,l,m,n是任意的非负整数,并证明了环的Brown-McCoy根与(1,1,1,1)-根,(1,1

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

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.