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We consider a total matric algebra M over a field F, whose general element is u = Yj a a e ih (h j = 1> * ' * > n )> where e^^ = ea if j = 1, and e^en = 0 for j^L THEOREM 1. A necessary and sufficient condition that u = ^La^e^ be idempotent in M is This is seen immediately on writing U ~2!_jO£psOtsqepq P,Q,s and comparing with U / jOLygepa» P,Q THEOREM 2. A necessary and sufficient condition f or an idempotent element u to be primitive in M is (2) a pi a jq = a pg (Xji, (p, q, i, j = 1, • •doi:10.1090/s0002-9904-1931-05279-4 fatcat:yzuuckh5fbc37oflsmjax5zmhq