Describing the Algebraic Hyperstructure of All Elements in Radiolytic Processes in Cement Medium Bijan Davvaz a , Akbar Dehghan Nezhad a , Mohammad Mazloum-Ardakani b and M. A. Sheikh-Mohsenei b a Department of Mathematics, Yazd University, Yazd, Iran davvaz@yazd.ac.ir , anezhad@yazd.ac.ir b Department of Chemistry, Yazd University, Yazd, Iran mazloum@yazd.ac.ir (Received June 27, 2013) Abstract Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of hyperstructures are the ones called H v -structures. In the present paper, the algebraic hyperstructures (H v - structures) are described for the elements in radiolytic processes in cement medium. These elements include e − aq , H 2 , OH − , H, O − , OH, H 2 O, HO − 2 , H 2 O 2 , O − 2 , O 2− 2 , HO 2 , O 2 , O − 3 , O 3 and O 2− which were reported by Bouniol and Bjergbakke, within a comprehensive model for describing radiolytic processes in cement medium. 1 Introduction Radicals (or free radicals) are atoms, molecules, or ions with unpaired electrons on an open shell configuration. These unpaired electrons cause radicals to be highly chemi- cally reactive. If the free electron strikes a water molecule, the ionized molecule will produce a free radical. Free radicals play an important role in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical pro- MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 72 (2014) 375-388 ISSN 0340 - 6253