Title: Essential cohomology for elementary abelian p-groups Authors: Fatma Altunbulak Aksu (Bilkent, Turkey) David J. Green (Jena, Germany) Date: 25 September 2008 Status: Submitted for publication MSC 2000: Primary 20J06; Secondary 13A50, 55S10 arXiv:0809.4425v1 [math.GR] Abstract: For an odd prime p the cohomology ring of an elementary abelian p-group is polynomial tensor exterior. We show that the ideal of essential classes is the Steenrod closure of the class generating the top exterior power. As a module over the polynomial algebra, the essential ideal is free on the set of Mui invariants.