TY - JOUR

T1 - Equivariant Total Ring of Fractions and Factoriality of Rings Generated by Semi-Invariants

AU - Hashimoto, Mitsuyasu

N1 - Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2015/4/3

Y1 - 2015/4/3

N2 - 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.

AB - 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.

KW - Character group

KW - Invariant subring

KW - UFD

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U2 - 10.1080/00927872.2013.867967

DO - 10.1080/00927872.2013.867967

M3 - Article

AN - SCOPUS:84923313285

VL - 43

SP - 1524

EP - 1562

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -