Abstract. As an extension of a result in [1] about the semisimple case, left orders in the sense of Fountain and Gould in rings with local units, minimum condition for principal left ideals, and arbitrary radical are characterized by means of covering every finite subset of them by left orders in the classical sense in rings with identity and with minimum condition for principal left ideals.

AMS Subject Classification (1991): 16P70, 16N40, 16U99

Received October 13, 1993. (Registered under 5566/2009.)