右弱C2环

RIGHT WEAKLY C2 RINGS

给出右弱C2环的定义,证明了:1)环R是右弱C2环当且仅当对每个0≠a∈R,存在正整数n使得a^n≠0,且若r(a^n)=r(e),其中e^2=e∈R,则e∈Ra^n;2)R是右弱C2环,则Zr(R)J(R);3)给出右弱C2环上Dedekind有限环的等价刻画;4)R是强正则环当且仅当R是右pp环,右弱C2环,Abel环和右零因子幂环.

The concept of right weak C2 rings is introduced in this note. The following results are shown: 1) R is a right weak C2 ring if and only if for every 0=a R, there exists a positive integer n such that a=0, and if r(a') = r(e), where e2 = e(=R, then e Ran: 2) If R is a right weak C2 ring, then Zr(R) J(R): 3) Some equivalent characterizations of Dedekind finiteness of right weak C2 rings are given : 4) R is a strongly regular ring if and only if R is a right pp ring, right weak C2 ring, Abelian ring and ring with right zero-divisor power.