摘要
本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.
Abstract In this note, we prove that if R is a reduced ring and A = R[T]/fR[T] is a finitely generated R-module, then f is a normal polynomial. Moreover, if R is connected, then the leading coefficient of / is a unit. It is also proved that a coherent connected ring with finite weak global dimension is a domain.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2002年第6期1171-1176,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(19771046)
关键词
多项式
平坦模
约化环
连通环
Polynomial
Flat module
Reduced ring
Connected ring
