OnJer 12: 91-J()6, J995 91 Kluwer AClulemic Pllhlishers. /'rillletl ÎI/ I/re Nelfwrlnllds. The Center of an Effect Algebra R. J. GREECHIE Deparlmelll of Tedl University , RUSIOI/, LA 71272 , U. S.A. D. FO ULIS Departmel/l of MalhemalÎCs and SlalÎslics , UllíversÎly of Massachusetts , Amhersl , MA 01003 , U. S. A. and S. P U L M A N N 0 V A Malhemalicai Insli /U le qf lhe Siovak Academy 01 Bralísiava, Siov(/kia (Received: 5 October 1994; accepted: 30 1994) Abstr.lct. An effcct algebra is a partial modeled on the effcct algebra of positive sclf- adjoint identity on a Hilbcrt effect is ordered in a by the partial order on the standard algcbra. An effect algebra is said to be if , as a posel , it forms a distributivc lattice. We dcfine and slUdy lhe ccnler of an effccl algebra , relate it to cartesian-product factorizatiolls , detenninc the cenler of lhe effect algebra, and characterize all fìnite distributive effecl algebras as products of chains and Mathematics Subject Classilicatiolls 06C 15 , Key words. Effect algebra, orlbosupplement, isolropic elemenl , principal center, íntcrval algebra, effcct ring, scale algebra, distribulive effccl algebra. 1. lnlroduction by the use of positive operator valued measures in stochastíc (or phase space) quantum 3 , 22, 25 , 26] and by the study of fuzzy or unsharp quantum 5 , 15 , 20] there has been a recent surge of interest ìn a new c1 ass of orthostructures called weak (or generalized) orthoalgebras [1 5 , difference (or D) poset:s [7-10, 13]. By and large , these structures are mathematica l1y equivalent , and it is mostJy a matter of taste which to selec t. ln what follows , we choose to focus on effect algebras because lhe additíve structure of such we l1 with the partially ordered abelian groups which often figure in their representation {2]. Thus , we assume that the reader is somewhat familiar with 12, 13] , convenience, we reproduce most of the pertinent basìc defìnitions and results.