线性 J-Armendariz 环

A ring R is called LJA ring if f (x )g (x )=0 implies a ib j ∈J (R )for all f (x )=a 0 +a 1 x , g (x)=b 0 +b 1 x in R [x ]and i ,j = 0,1,where J (R )is the Jacobson radical of R.Considering the properties of LJA rings and the relationship between such rings and other related rings,the author gives simple examples of an infinite direct product of 2-primal rings not to be a 2-primal ring,and proves that Koethe’s conjecture has a positive solution if and only if a polynomial ring over any NI ring is an LJA ring.