journal6 ›› 2012, Vol. 33 ›› Issue (6): 22-25.DOI: 10.3969/j.issn.1007-2985.2012.06.006

• Mathematics • Previous Articles     Next Articles

I-Adic Topology and Two Lemmas of Hilbert Basis Theorem


  1. (Basic Courses Department,Fujian Communications Technology College,Fuzhou 350007,Fujian China)
  • Online:2012-11-25 Published:2013-01-14

Abstract: 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 investigated.

Key words: I-adic topology, completion, formal power series ring, noetherian ring

WeChat e-book chaoxing Mobile QQ