The Tensor Products of Nilrings with Bounded Index of Nilpotence

R is a ring, for any nilpotent element r∈R if there exists a fixed integer nsuch that r~n=0, then R is said to be with bounded index of nilpotence, theleast of such integer n is called the index of R, denoted by i(R). If R is a nil ring with bounded index i(R)=n, R′ is a commutative ring,A·A·Klein〔1〕 has discussed the property of bounded index of nilpotence of RR′. In this paper we shall discuss the properties of bounhed index of nil-potence of RR′ when R′ is not commutative.