On the surjectivity of some trace maps

Eli Aljadeff

doi:10.1007/BF02773679

On the surjectivity of some trace maps

Eli Aljadeff^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let K be a commutative ring with a unit element 1. Let Γ be a finite group acting on K via a map t: Γ→Aut(K). For every subgroup H≤Γ define tr_H :K→K^H by tr_h (x)=Σ_σ∈H σ(x). We prove Theorem: tr_Γ is surjective onto K^Γ if and only if tr_P is surjective onto K^P for every (cyclic) prime order subgroup P of Γ. This is false for certain non-commutative rings K.

Original language	English
Pages (from-to)	221-232
Number of pages	12
Journal	Israel Journal of Mathematics
Volume	86
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02773679
State	Published - Oct 1994
Externally published	Yes

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abstract = "Let K be a commutative ring with a unit element 1. Let Γ be a finite group acting on K via a map t: Γ→Aut(K). For every subgroup H≤Γ define tr H :K→K H by tr h (x)=Σσ∈H σ(x). We prove Theorem: trΓ is surjective onto K Γ if and only if tr P is surjective onto K P for every (cyclic) prime order subgroup P of Γ. This is false for certain non-commutative rings K.",

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N2 - Let K be a commutative ring with a unit element 1. Let Γ be a finite group acting on K via a map t: Γ→Aut(K). For every subgroup H≤Γ define tr H :K→K H by tr h (x)=Σσ∈H σ(x). We prove Theorem: trΓ is surjective onto K Γ if and only if tr P is surjective onto K P for every (cyclic) prime order subgroup P of Γ. This is false for certain non-commutative rings K.

AB - Let K be a commutative ring with a unit element 1. Let Γ be a finite group acting on K via a map t: Γ→Aut(K). For every subgroup H≤Γ define tr H :K→K H by tr h (x)=Σσ∈H σ(x). We prove Theorem: trΓ is surjective onto K Γ if and only if tr P is surjective onto K P for every (cyclic) prime order subgroup P of Γ. This is false for certain non-commutative rings K.

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ER -

On the surjectivity of some trace maps

Abstract

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