On finite generation of R-subalgebras of R[X]

JOURNAL OF ALGEBRA

卷:320

Article

Dutta, Amartya K.²  Onoda, Nobuharu¹ 

[1] Univ Fukui, Dept Math, Fukui 9108507, Japan

[2] Indian Stat Inst, Stat Math Unit, Kolkata 700108, India

关键词: finite generation;    subalgebra of polynomial algebra;    dimension formula;    Nagata ring;    discrete valuation ring;    complete local ring;    Krull domain;   

DOI  :  10.1016/j.jalgebra.2008.02.013

来源: Elsevier

【 摘 要 】

We show that over a complete discrete valuation ring R whose residue field is algebraically closed, any Noetherian R-subalgebra of R[X] is finitely generated and present examples of non-finitely generated Noetherian R-subalgebras of R[X] satisfying various properties. We also give a sufficient codimension-one criterion for a Noetherian R-subalgebra of R[X] to be finitely generated over R when R is locally factorial. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free