Zahra Keshtkar

Shahid Chamran University of Ahvaz | scu · Department of Mathematics

We return to the work of Banaschewski and extract from it a theorem of Fuchs, Heinzer, and Olberding. As an application of Fuchs-Heinzer-Olberding's theorem, we generalize a result of Gillman and Kohls. We study pseudo-irreducible ideals and show that every ideal of a pm-ring is the (not necessarily finite) intersection of pairwise comaximal pseudo...

A similar characterization, as the Gelfand-Kolmogoroff theorem for the maximal ideals in C(X), is given for the maximal ideals of Cc(X). It is observed that the zc-ideals in Cc(X) are contractions of the z-ideals of C(X). Using this, it turns out that maximal ideals (respectively, prime zc-ideals) of Cc(X) are precisely the contractions of maximal...

A similar characterization, as the Gelfand-Kolmogoroff theorem for the maximal ideals in C(X), is given for the maximal ideals of Cc(X). It is observed that the zc-ideals in Cc(X) are contractions of the zideals of C(X). Using this, it turns out that maximal ideals (respectively, prime zc-ideals) of Cc(X) are precisely the contractions of maximal i...

The c-realcompact spaces are fully studied and most of the important and well-known properties of realcompact spaces are extended to these spaces. For a zero-dimensional space X, the space υ0X, which is the counterpart of υX, the Hewitt realcompactification of X, is introduced and studied. It is shown that υ0X, which is the smallest c-realcompact s...