Sezer, M.2016-02-082016-02-0820150021-8693http://hdl.handle.net/11693/22625We consider the ring of coinvariants for a modular representation of a cyclic group of prime order p. We show that the classes of the terminal variables in the coinvariants have nilpotency degree p and that the coinvariants are a free module over the subalgebra generated by these classes. An incidental result we have is a description of a Gröbner basis for the Hilbert ideal and a decomposition of the corresponding monomial basis for the coinvariants with respect to the monomials in the terminal variables. © 2014 Elsevier Inc.EnglishCoinvariantsModular actionsArticle10.1016/j.jalgebra.2014.08.0591090-266X