On the mappings 𝒵 A and ℑ A in intermediate rings of C ( X )

Mehdi Parsinia

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 383-390
  • ISSN: 0010-2628

Abstract

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In this article, we investigate new topological descriptions for two well-known mappings 𝒵 A and ℑ A defined on intermediate rings A ( X ) of C ( X ) . Using this, coincidence of each two classes of z -ideals, 𝒵 A -ideals and ℑ A -ideals of A ( X ) is studied. Moreover, we answer five questions concerning the mapping ℑ A raised in [J. Sack, S. Watson, C and C * among intermediate rings, Topology Proc. 43 (2014), 69–82].

How to cite

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Parsinia, Mehdi. "On the mappings ${\mathcal {Z}}_A$ and $\Im _A$ in intermediate rings of $C(X)$." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 383-390. <http://eudml.org/doc/294777>.

@article{Parsinia2018,
abstract = {In this article, we investigate new topological descriptions for two well-known mappings $\{\mathcal \{Z\}\}_A$ and $\Im _A$ defined on intermediate rings $A(X)$ of $C(X)$. Using this, coincidence of each two classes of $z$-ideals, $\{\mathcal \{Z\}\}_A$-ideals and $\Im _A$-ideals of $A(X)$ is studied. Moreover, we answer five questions concerning the mapping $\Im _A$ raised in [J. Sack, S. Watson, $C$ and $C^*$ among intermediate rings, Topology Proc. 43 (2014), 69–82].},
author = {Parsinia, Mehdi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$z$-ideal; $\{\mathcal \{Z\}\}_A$-ideal; $\Im _A$-ideal; $z$-filter; $\{\mathcal \{Z\}\}_A$-filter; $\Im _A$-filter; intermediate ring},
language = {eng},
number = {3},
pages = {383-390},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the mappings $\{\mathcal \{Z\}\}_A$ and $\Im _A$ in intermediate rings of $C(X)$},
url = {http://eudml.org/doc/294777},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Parsinia, Mehdi
TI - On the mappings ${\mathcal {Z}}_A$ and $\Im _A$ in intermediate rings of $C(X)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 383
EP - 390
AB - In this article, we investigate new topological descriptions for two well-known mappings ${\mathcal {Z}}_A$ and $\Im _A$ defined on intermediate rings $A(X)$ of $C(X)$. Using this, coincidence of each two classes of $z$-ideals, ${\mathcal {Z}}_A$-ideals and $\Im _A$-ideals of $A(X)$ is studied. Moreover, we answer five questions concerning the mapping $\Im _A$ raised in [J. Sack, S. Watson, $C$ and $C^*$ among intermediate rings, Topology Proc. 43 (2014), 69–82].
LA - eng
KW - $z$-ideal; ${\mathcal {Z}}_A$-ideal; $\Im _A$-ideal; $z$-filter; ${\mathcal {Z}}_A$-filter; $\Im _A$-filter; intermediate ring
UR - http://eudml.org/doc/294777
ER -

References

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  2. Aliabad A. R., Parsinia M., z R -ideals and z R ∘ -ideals in subrings of ℝ X , to appear in Iranian J. Math. Sci. Inform. 
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  7. Murray W., Sack J., Watson S., P -spaces and intermediate rings of continuous functions, Rocky Mountain J. Math. 47 (2017), no. 8, 2757–2775. MR3760317
  8. Panman P., Sack J., Watson S., Correspondence between ideals and z-filters for rings of continuous functions between C * and C , Comment. Math. 52 (2012), no. 1, 11–20. MR2977710
  9. Parsinia M., Remarks on L B I -subalgebras of C ( X ) , Comment. Math. Univ. Carolin. 57 (2016), no. 2, 261–270. MR3513449
  10. Parsinia M., Remarks on intermediate C -rings of C ( X ) , Quaest. Math. (online 2017), 8 pages. MR3836415
  11. Plank D., 10.4064/fm-64-1-41-54, Fund. Math. 64 (1969), 41–54. MR0244953DOI10.4064/fm-64-1-41-54
  12. Redlin L., Watson S., Maximal ideals in subalgebras of C ( X ) , Proc. Amer. Math. Soc. 100 (1987), no. 4, 763–766. Zbl0622.54011MR0894451
  13. Sack J., Watson S., C and C * among intermediate rings, Topology Proc. 43 (2014), 69–82. MR3080750
  14. Sack J., Watson S., Characterizing C ( X ) among intermediate C -rings on X , Topology Proc. 45 (2015), 301–313. MR3291114

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