When is the set of d-ideals of a C(X) closed under addition?
by
Melvin Henriksen
Harvey Mudd College
Coauthors: F. Azarpanah

X will denote a Tychonoff space, and C(X) the algebra of continuous real-valued functions on X. If S subset C(X), let S^d = { f in C(X): fS={0} }. An ideal I of C(X) such that a in I implies a^dd subset I a d-ideal. In their paper On z^o-ideals in C(X), Fund. Math. 160 (1999), 15-25, Azarpanah, Karamzadeh, and Rezai Aliabad posed the question of the title using different notation. X is called a quasi-F space if its dense cozerosets are C ^* -embedded. Our main result is that X satisfies the conditions of the title if and only if it is a quasi-F space. This enables us to establish new results about quasi-F spaces as well as results on the spaces of the title that are not evident. Some, but not all results apply to \Phi-algebras (i.e., archimedean lattice-ordered algebras with an identity element that is a weak order unit.)

Date received: June 26, 2000