Multiplicative Invariants and the Finite Co‐Hopfian Property
نویسندگان
چکیده
منابع مشابه
On the Cohen-macaulay Property of Multiplicative Invariants
We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras k[x 1 , . . . , x ±1 n ] that stabilize the multiplicative group consisting of all monomials in the variables xi. For the most part, we concentrate on the case where the base ring k is Z. Our main result states tha...
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Let G be a nite subgroup of GL d (Z). Then G acts on the Laurent polynomial ring kX 1 1 d ] over the eld k via the natural G-action on the multiplicative group generated by the variables X 1 ; : : : ; X d (= Z d). We show that the class group of the ring of invariants of this action is isomorphic to Hom(G=N;k) H 1 (G=D; (Z d) D), where N denotes the subgroup of G that is generated by all reeect...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2009
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579300000978