2004/09/07 by Müfit Sezer, Müfi̇t Sezer, Sezer, Müfit +2
Mathematics · #13A50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.AC #math.GR #msc:13A50
paper · pdf · doi:10.48550/arxiv.math/0409107
arxiv created 2004/09/07 · openalex publication_date 2004/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gröbner basis for the Hilbert ideal and the corresponding monomial basis for the coinvariants. We also describe the decomposition of the coinvariants as a module over the group ring. For one family of representations, we are able to describe the coinvariants despite the fact that an explicit generating set for the invariants is not known. In all cases our results confirm the conjecture of Harm Derksen and Gregor Kemper on degree bounds for generators of the Hilbert ideal. As an incidental result, we identify the coefficients of the monomials appearing in the orbit product of a terminal variable for the three dimensional indecomposable representation.