Geodesic
On m-closure of ideals in a class of subrings of C(X)
Filomat, Tome 37 (2023) no. 12, p. 3907

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

A subalgebra A(X) of C(X) is said to be a β-subalgebra if it is closed under bounded inversion and the space of its maximal ideals equipped with the hull-kernel topology is homeomorphic to βX 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 β-subalgebras which is shown to be a larger class than intermediate rings. We also study a more extended class of subrings than β-subalgebras, namely, LBI-subalgebras, and characterize the conditions under which an LBI-subalgebra is a β-subalgebra. Moreover, some known facts in the context of C(X) and intermediate rings of C(X) are generalized to β-subalgebras.
DOI : 10.2298/FIL2312907E
Classification : 54C30, 46E25
Keywords: LBI-subalgebra, β-subalgebra, m-topology, m-closure 
Masoumeh Etebar; Mehdi Parsinia. On m-closure of ideals in a class of subrings of C(X). Filomat, Tome 37 (2023) no. 12, p. 3907 . doi: 10.2298/FIL2312907E
@article{10_2298_FIL2312907E,
     author = {Masoumeh Etebar and Mehdi Parsinia},
     title = {On m-closure of ideals in a class of subrings of {C(X)}},
     journal = {Filomat},
     pages = {3907 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312907E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312907E/}
}
TY  - JOUR
AU  - Masoumeh Etebar
AU  - Mehdi Parsinia
TI  - On m-closure of ideals in a class of subrings of C(X)
JO  - Filomat
PY  - 2023
SP  - 3907 
VL  - 37
IS  - 12
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2312907E/
DO  - 10.2298/FIL2312907E
LA  - en
ID  - 10_2298_FIL2312907E
ER  - 
%0 Journal Article
%A Masoumeh Etebar
%A Mehdi Parsinia
%T On m-closure of ideals in a class of subrings of C(X)
%J Filomat
%D 2023
%P 3907 
%V 37
%N 12
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2312907E/
%R 10.2298/FIL2312907E
%G en
%F 10_2298_FIL2312907E

Cité par Sources :