【摘要】 本文着重讨论具有性质D(n,z)的质环的可换性.证明了若R是具有性质D(n,z)的质环,而charR≠2;或charR=2,(?)~2≠0;或charR=2且对R的所有幂等元e,性质D(n,z)中的n=n(e,e)都是偶数,那么R为可换整环或为除环.此外,文中给出了具有性质D(n,1)和具有性质D(2,z)的质环的可换性的有关结果.更多还原

【Abstract】 Let R be an associative ring, ann 3 be a nonzero deri-vation of R. Suppose that, for all x,y∈R, there exist an integer n（x,y）>1 and a z_x,y in the center of R such that [x,y]^n（x,y）z_x,y=[x,y] we call such a ring R a ring with property D（n.z）. In this paper we have proved: 1) Let R be a prime ring with property D（n.z）. If i) the characteristic of R is not 2; or ii) the characteristic of R is 2, and 2≠0; or iii) the characteristic of R is 2, and n = n（e,e） in property D（n, z） is an even number for all idempotent e of R. Then either R is a commutative domain ring or a division ring. 2) If a prime ring R has property D（n,1）, then R either is a commutative domain ring or is a 4—dimensional simple algebra. 3) If a prime ring R has property D（2,z）, then R is a commutative domain ring.更多还原