Integral Extensions by a PI-ring and Jacobson Rings

• Main Authors: Wan-Yu Tsai, 蔡宛育
• Other Authors: 莊正良
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/10065448151875823450

碩士 === 國立臺灣大學 === 數學研究所 === 93 === Abstract In this paper the main theorems are as follows: (i) Assume S = RCS(R), S is a module- nite extension of R if and only if CS(R) is a PI-ring and the ring extension S=R is ring- nite and integral. (ii) Let S R be prime rings and S is a ring- nite centralizing extension of R by a PI-ring. Then S is a G-ring if and only if R is a G-ring and S is algebraic over R. (iii) If the ring R is a ~J-ring, then any ring- nite centralizing extension S of R by a PI-ring is also a ~J-ring.