Affineness on Noetherian graded rings, algebras and Hopf algebras

In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine.

Publication Details

Journal
ArXiv.org
Published
2025-03-15
Primary Topic
Advanced Topics in Algebra
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Affineness on Noetherian graded rings, algebras and Hopf algebras

ArXiv.org
Advanced Topics in Algebra
article

Affineness on Noetherian graded rings, algebras and Hopf algebras

article en

Abstract

In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine.

ArXiv.org
Openalex Percentile: Top 35%
Advanced Topics in Algebra
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Affineness on Noetherian graded rings, algebras and Hopf algebras · ArXiv.org (2025) | TGRS Research Map | TGRS