$C(X)$ can sometimes determine $X$ without $X$ being realcompact

Melvin Henriksen; Biswajit Mitra

Displaying similar documents to “ $C (X)$ can sometimes determine $X$ without $X$ being realcompact”

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Pierre Matet (2013)

Fundamenta Mathematicae

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We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_{κ} (λ)$ that is normal.

Two remarks on the maximal-ideal space of H $^{\infty}$

Stephen Scheinberg (2021)

Commentationes Mathematicae Universitatis Carolinae

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The topology of the maximal-ideal space of $H^{\infty}$ is discussed.

Rings of continuous functions vanishing at infinity

Ali Rezaei Aliabad, F. Azarpanah, M. Namdari (2004)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a Hausdorff space $X$ is locally compact if and only if its topology coincides with the weak topology induced by $C_{\infty} (X)$ . It is shown that for a Hausdorff space $X$ , there exists a locally compact Hausdorff space $Y$ such that $C_{\infty} (X) ≅ C_{\infty} (Y)$ . It is also shown that for locally compact spaces $X$ and $Y$ , $C_{\infty} (X) ≅ C_{\infty} (Y)$ if and only if $X ≅ Y$ . Prime ideals in $C_{\infty} (X)$ are uniquely represented by a class of prime ideals in $C^{*} (X)$ . $\infty$ -compact spaces are introduced and it turns out that a locally compact space $X$ is $\infty$ -compact if and only...

The ideal (a) is not $G_{δ}$ generated

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

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We prove that the ideal (a) defined by the density topology is not $G_{δ}$ generated. This answers a question of Z. Grande and E. Strońska.

On wsq-primary ideals

Emel Aslankarayiğit Uğurlu, El Mehdi Bouba, Ünsal Tekir, Suat Koç (2023)

Czechoslovak Mathematical Journal

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We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$ . The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0 \neq a b \in Q$ for some $a, b \in R$ , then $a^{2} \in Q$ or $b \in \sqrt{Q} .$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero...

Erratum to $(δ, 2)$ -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

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

F. Azarpanah, O. A. S. Karamzadeh, S. Rahmati (2008)

Colloquium Mathematicae

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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 $d i m (C (X) / C_{F} (X)) \geq d i m C (X)$ , 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....

Displaying similar documents to “ C ( X ) can sometimes determine X without X being realcompact”

Normal restrictions of the noncofinal ideal on P κ ( λ )

Two remarks on the maximal-ideal space of H ∞

Rings of continuous functions vanishing at infinity

The ideal (a) is not G δ generated

On wsq-primary ideals

Erratum to ( δ , 2 ) -primary ideals of a commutative ring

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

Displaying similar documents to “ $C (X)$ can sometimes determine $X$ without $X$ being realcompact”

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Two remarks on the maximal-ideal space of H $^{\infty}$

The ideal (a) is not $G_{δ}$ generated

Erratum to $(δ, 2)$ -primary ideals of a commutative ring