I-adic拓扑与希尔伯特basis定理的2个推论  

Ⅰ-Adic Topology and Two Lemmas of Hilbert Basis Theorem

作　　者：任芳 

机构地区：[1]福建船政交通职业技术学院基础部,福建福州350007

出　　处：《吉首大学学报（自然科学版）》2012年第6期22-25,46,共5页Journal of Jishou University(Natural Sciences Edition)

摘　　要：首先证明交换环关于Ⅰ-adic拓扑诱导的完备化环是商环的有限投射极限,其次揭示Abel范畴noetherian对象与正合序列的关系,进而用范畴的方法给出希尔伯特basis定理的推论——noetherian环的Ⅰ-adic拓扑完备化环Rnoetherian环的新证明,之后论证该推论与希尔伯特basis定理的另一推论是等价的.This paper first shows that the completion of a commutative ring induced by I-adic topology is the finite projective limit of its quotient rings. And then the relationship between noetherian objects and exact sequences is given; moreover,a new proof for the lemma of Hilbert basis theorem is presented, which states that：the completion of a noetherian ring induced by I-adic topology is again a noetherian ring. Also, the equivalence of the above lemma and the other lemma of Hilbert basis theorem is investiga- ted.

关 键 词：Ⅰ-adic拓扑 完备化 形式幂级数环 noetherian环 

分 类 号：O154[理学—数学]