%0 Journal Article
%A REN Fang
%T *I*-Adic Topology and Two Lemmas of Hilbert Basis Theorem
%D 2012
%R 10.3969/j.issn.1007-2985.2012.06.006
%J Journal of Jishou University(Natural Sciences Edition)
%P 22-25
%V 33
%N 6
%X 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.
%U https://zkxb.jsu.edu.cn/EN/10.3969/j.issn.1007-2985.2012.06.006