Vol. 36, No. 3, 1971

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Rings of quotients of Φ-algebras

Donald Glen Johnson

Vol. 36 (1971), No. 3, 693–699

Let be a completely regular (Hausdorff) space. Fine, Gillman, and Lambek have studied the (generalized) rings of quotients of C() = C(;R), with particular emphasis on the maximal ring of quotients, Q(). In this note, we start with a characterization of Q() that differs only slightly from one of theirs. This characterization is easily altered to fit more general circumstances, and so serves to obtain some results on non-maximal rings of quotients of C(), and to generalize these results to the class of Φ-algebras.

Mathematical Subject Classification
Primary: 46.25
Secondary: 54.00
Received: 13 April 1970
Published: 1 March 1971
Donald Glen Johnson