Sezer, M.2015-07-282015-07-2820110026-9255http://hdl.handle.net/11693/12070We consider a diagonal action of a cyclic group of prime order on a polynomial ring F[x1,...,xn]. We give a description of the actions for which the corresponding Hilbert ideal is Gotzmann when n = 2. Nevertheless, we show that there is a separating set of invariant monomials that generates a proper lexsegment ideal in the polynomial ring for all n. As well, we provide an algorithm to compute this set. © 2009 Springer-Verlag.EnglishGotzmann idealsLexsegment idealsSeparating invariantsArticle10.1007/s00605-009-0182-31436-5081