Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

C(X) vs. C(X) modulo its socle

100%

Azarpanah F., Karamzadeh O., Rahmati S.

Colloquium Mathematicum

2008

tom 111

nr 2

315-336

Let $C_{F}(X)$ be the socle of C(X). It is shown that each prime ideal in $C(X)/C_{F}(X)$ is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that $dim (C(X)/C_{F}(X)) ≥ dim C(X)$, where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential ideal E in C(X), we observe that $E/C_{F}(X)$ is essential in $C(X)/C_{F}(X)$ if and only if the set of isolated points of X is finite. Finally, we characterize topological spaces X for which the Jacobson radical of $C(X)/C_{F}(X)$ is zero, and as a consequence we observe that the cardinality of a discrete space X is nonmeasurable if and only if υX, the realcompactification of X, is first countable.

Erratum to: "C(X) vs. C(X) modulo its socle" (Colloq. Math. 111 (2008), 315-336)

100%

Azarpanah F., Karamzadeh O., Rahmati S.

Colloquium Mathematicum

2015

tom 139

nr 1

147-148

Ograniczanie wyników

2 Colloquium Mathematicum

2 Azarpanah F.

2 Karamzadeh O.

2 Rahmati S.

1 2015

1 2008

Wyniki wyszukiwania

C(X) vs. C(X) modulo its socle

Erratum to: "C(X) vs. C(X) modulo its socle" (Colloq. Math. 111 (2008), 315-336)