给出JTT环的定义,研究JTT环的一些性质,主要证明了如下结果:1)R为JTT环当且仅当对任意a∈N(R),x∈R,有a2 x=axa;2)R为交换约化环当且仅当V3(R)是JTT环;3)R为JTT环且a∈aRa,则存在c∈R,使得a=ca2;4)设R为JTT环,则对任意e∈E(R),a∈R,有(1-e)aeR(1-e)ae=0.
In this paper, the definition of JTT ring is given and some properties of JTT rings are studied. The proved results are as follows. 1) a ring R is a JTT ring if and only if a^2x=axa for each xER and a ∈N(R) ; 2) R is a commutative reduced ring if and only if V3 (R) is a JTT ring; 3) if R is a JTT ring and a∈aRa, then a=ca^2 for some c∈R; 4) if R is a JTT ring, then (1- e)aeR(1- e)ae=0 for each e∈ E(R) and a∈ R.