Graded integral domains and Nagata rings

JOURNAL OF ALGEBRA

卷:387

Article

Anderson, David F.¹  Chang, Gyu Whan² 

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Incheon, Dept Math, Inchon 406772, South Korea

关键词: Graded integral domain;    t-Operation;    Nagata ring;    PvMD;    Kronecker function ring;   

DOI  :  10.1016/j.jalgebra.2013.04.021

来源: Elsevier

【 摘 要 】

Let R = circle plus(alpha is an element of Gamma) R-alpha be an integral domain graded by an arbitrary torsionless grading monoid Gamma. For any f is an element of R, let C(f) be the ideal of R generated by the homogeneous components of f, and let N(H) = {g is an element of R vertical bar C(g)(v) = R}. In this paper, we study relationships between the ideal-theoretic properties of R-N(H) and the homogeneous ideal-theoretic properties of R. For example, we show that R is a graded Krull domain if and only if R-N(H) is a Dedekind domain, if and only if R-N(H) is a PID; and that if R contains a unit of nonzero degree, then R is a PvMD if and only if R-N(H) is a Prufer domain, if and only if each ideal of R-N(H) is extended from a homogeneous ideal of R. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free