On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$

Parsinia, Mehdi

doi:10.14712/1213-7243.2015.249

Commentationes Mathematicae Universitatis Carolinae

2018

DOI: 10.14712/1213-7243.2015.249

|View full text |Cite

On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$

Mehdi Parsinia¹

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On m-closure of ideals in a class of subrings of C(X)

Etebar,

Parsinia

2023

Filomat

View full text Add to dashboard Cite

A subalgebra A(X) of C(X) is said to be a ?-subalgebra if it is closed under bounded inversion and the space of its maximal ideals equipped with the hull-kernel topology is homeomorphic to ?X with a homeomorphism which leaves X pointwise fixed. Kharbhih and Dutta in [Closure formula for ideals in intermediate rings, Appl. Gen. Topol. 21 (2) (2020), 195-200] showed that the closure of every ideal I of an intermediate ring with the m-topology, briefly, the m-closure of I, equals the intersection of all maximal ideals in A(X) containing I. In this paper, we extend this fact to the class of ?-subalgebras which is shown to be a larger class than intermediate rings. We also study a more extended class of subrings than ?-subalgebras, namely, LBI-subalgebras, and characterize the conditions under which an LBI-subalgebra is a ?-subalgebra. Moreover, some known facts in the context of C(X) and intermediate rings of C(X) are generalized to ?-subalgebras.

show abstract

On m-closure of ideals in a class of subrings of C(X)

Etebar,

Parsinia

2023

Filomat

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 1 publication

References 6 publications

On m-closure of ideals in a class of subrings of C(X)

On m-closure of ideals in a class of subrings of C(X)

Contact Info

Product

Resources

About