Graded integral domains whose nonzero homogeneous ideals are invertible-Reference-Cited by-同舟云学术

Graded integral domains whose nonzero homogeneous ideals are invertible

Published:2016-11 Issue:07 Volume:26 Page:1361-1368
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Anderson David F.¹,Chang Gyu Whan²

Affiliation:

1. Department of Mathematics, The University of Tennessee, Knoxville, TN 37996-1320, USA

2. Department of Mathematics Education, Incheon National University, Incheon 22012, Republic of Korea

Abstract

Let [Formula: see text] be an integral domain graded by a nontrivial torsionless grading monoid [Formula: see text]. Among other things, we show that if [Formula: see text], then every nonzero homogeneous ideal of [Formula: see text] is invertible if and only if [Formula: see text] is a field and [Formula: see text], where [Formula: see text] is an indeterminate over [Formula: see text], if and only if [Formula: see text] is a Dedekind domain, if and only if [Formula: see text] is a PID.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196716500582

Reference12 articles.

1. Divisibility Properties of Graded Domains

2. Graded krull domains

3. Homogeneous splitting sets of a graded integral domain

4. Graded integral domains and Nagata rings

5. Dedekind domains and graded rings

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