Number systems which satisfy part but not allof the postulates for a field are called subvarietiesof a field. The purpose of this paper is the determinationof as great as possible a number of suchvarieties by suitable definitions of the class ofelements and of the two operations involved.
Two postulate systems are considered. The firstgives rise to 284 varieties, instances of all of whichare given for infinite classes of elements, and of allexcept three for finite classes.
Of the 8192 combinations of postulates arisingfrom the second system, not more than 1146 can beconsistent. Instances are given of 1054 of these.As the postulates of this system are not independent,no conclusion has been reached regarding the remainingcases.
