Some Applications of André–Quillen Homology to Classes of Arithmetic Rings

Let D be an integral domain and ⋆ a star operation defined on D. We say that D is a ⋆-power conductor domain (⋆-PCD) if for each pair a, b ∈ D\(0) and for each positive integer n we have Da n ∩ Db n = ((Da ∩ Db) n ) ⋆ . We study ⋆-PCDs and characterize them as root closed domains satisfying ((a, b) n ) −1 = (((a, b) −1 ) n ) ⋆ for all nonzero a, b and all natural numbers n ≥ 1. From this it follows easily that Prüfer domains are d-PCDs (where d denotes the trivial star operation), and v-domains (e.g., Krull domains) are v-PCDs. We also consider when a ⋆-PCD is completely integrally closed, and this leads to new characterizations of Krulll domains. In particular, we show that a Noetherian domain is a Krull domain if and only if it is a w-PCD.Date: May 15, 2019. MSC 2010: 13A05, 13A15, 13E05, 13F05, 13G05.

show abstract

On the structure of ⋆-power conductor domains

Anderson

Houston

Zafrullah

2019

Communications in Algebra

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Some Applications of André–Quillen Homology to Classes of Arithmetic Rings

Abstract: We compute the first André-Quillen homology modules for the simple over-rings of integrally closed domains and study an ideal theoretic condition arising from the vanishing of H1.

Cited by 1 publication

References 8 publications

On the structure of ⋆-power conductor domains

On the structure of ⋆-power conductor domains

Contact Info

Product

Resources

About