Equivariant Total Ring of Fractions and Factoriality of Rings Generated by Semi-Invariants

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Utilizing this machinery, we give some new criteria for factoriality (unique factorization domain property) of (semi-)invariant subrings under the action of affine algebraic groups, generalizing a result of Popov. We also prove some variations of classical results on factoriality of (semi-)invariant subrings. Some results over an algebraically closed base field are generalized to those over an arbitrary base field.

Let F be an affine flat group scheme over a commutative ring R, and S an F-algebra (an R-algebra on which F acts). We define an equivariant analogue Q F(S) of the total ring of fractions Q(S) of S. It is the largest F-algebra T such that S ⊂ T ⊂ Q(S), and S is an F-subalgebra of T. We study some basic properties.

Original languageEnglish
Pages (from-to)1524-1562
Number of pages39
JournalCommunications in Algebra
Volume43
Issue number4
DOIs
Publication statusPublished - Apr 3 2015
Externally publishedYes

Fingerprint

Semi-invariants
Equivariant
F-algebra
Subring
Ring
Unique factorisation domain
Affine Group
Group Scheme
Q-analogue
Algebraic Groups
Algebraically closed
Commutative Ring
Subalgebra
Algebra
Arbitrary

Keywords

  • Character group
  • Invariant subring
  • UFD

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Equivariant Total Ring of Fractions and Factoriality of Rings Generated by Semi-Invariants. / Hashimoto, Mitsuyasu.

In: Communications in Algebra, Vol. 43, No. 4, 03.04.2015, p. 1524-1562.

Research output: Contribution to journalArticle

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