Geodesic
Remarks on the ring B1 (X)
Filomat, Tome 37 (2023) no. 19, p. 6453

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DOI

Let X be a nonempty topological space, C(X) F be the set of all real-valued functions on X which are discontinuous at most on a finite set and B 1 (X) be the ring of all real-valued Baire one functions on X. We show that any member of B 1 (X) is a zero divisor or a unit. We give an algebraic characterization of X when for every p ∈ X, there exists f ∈ B 1 (X) such that {p} = f −1 (0) and we give some topological characterizations of minimal ideals, essential ideals and socle of B 1 (X). Some relations between C(X) F, B 1 (X) and some interesting function rings on X are studied and investigated. We show that B 1 (X) is a regular ring if and only if every countable intersection of cozero sets of continuous functions can be represented as a countable union of zero sets of continuous functions.
DOI : 10.2298/FIL2319453A
Classification : 40C05, 46A45 54C40, 13C99
Keywords: Baire one functions, P-space, Minimal ideal, Fixed ideal, B1(X) 
Mohammad Reza Ahmadi ; and; Zahra Khosravi. Remarks on the ring B1 (X). Filomat, Tome 37 (2023) no. 19, p. 6453 . doi: 10.2298/FIL2319453A
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     author = {Mohammad Reza Ahmadi  and and and Zahra Khosravi},
     title = {Remarks on the ring {B1} {(X)}},
     journal = {Filomat},
     pages = {6453 },
     year = {2023},
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     number = {19},
     doi = {10.2298/FIL2319453A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2319453A/}
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