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Licensed Unlicensed Requires Authentication Published by De Gruyter March 20, 2020

Degree bounds for modular covariants

Jonathan Elmer ORCID logo and Müfit Sezer
From the journal Forum Mathematicum

Abstract

Let V,W be representations of a cyclic group G of prime order p over a field 𝕜 of characteristic p. The module of covariants 𝕜[V,W]G is the set of G-equivariant polynomial maps VW, and is a module over 𝕜[V]G. We give a formula for the Noether bound β(𝕜[V,W]G,𝕜[V]G), i.e. the minimal degree d such that 𝕜[V,W]G is generated over 𝕜[V]G by elements of degree at most d.

MSC 2010: 13A50

Communicated by Frederick R. Cohen


Funding statement: The second author is supported by a grant from TÜBITAK:119F181.

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Received: 2019-07-25
Revised: 2020-01-30
Published Online: 2020-03-20
Published in Print: 2020-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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