Vol. 71, No. 2, 1977

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Projective ideals in rings of continuous functions

James Glenn Brookshear

Vol. 71 (1977), No. 2, 313–333

An ideal in a ring Λ is said to be projective provided it is a projective Λ-module. This paper is concerned with the problem of topologically characterizing projectivity within the class of ideals of a ring of continuous functions. Since there are projective and nonprojective ideals having the same z-filter, the possibility of such a characterization appears remote. However, such a characterization is shown to exist for the projective z-ideals. Moreover, a relationship between projective z-ideals and arbitrary projective ideals is exhibited and used to show that, in some cases, every projective ideal is module isomorphic to a projective z-ideal.

Mathematical Subject Classification 2000
Primary: 54C40
Received: 6 February 1976
Revised: 2 February 1977
Published: 1 August 1977
James Glenn Brookshear