• Corpus ID: 235731754

# Common properties of some function rings on a topological space

```@inproceedings{Zand2021CommonPO,
title={Common properties of some function rings on a topological space},
year={2021}
}```
For a nonempty topological space X, the ring of all real-valued functions on X with pointwise addition and multiplication is denoted by F (X) and continuous members of F (X) is denoted by C(X). Let A(X) be a subring of F (X) and B be a non-zero and nonempty subset of A(X). Then we show that there are a subset S of X and a ring homomorphism φ : A(X) → A(S) such that kerφ = Ann(B). A lattice ordered subring A(X) of F (X) is called P -convex if every prime ideal of A(X) is an absolutely convex…

## References

SHOWING 1-10 OF 11 REFERENCES
Topics In Rings of Baire one functions and some function rings
• Mathematics
• 2021
Let X be a nonempty topological space and F (X) be the ring of all real-valued functions on X with pointwise addition and multiplication. Continuous members of F (X) is denoted by C(X) and C(X)F = {f
Remarks on the rings of functions which have a finite numb er of di scontinuities
• Mathematics
• 2021
Let X be an arbitrary topological space. F (X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F (X) such that f is discontinuous at most on a finite set. It is
Ideals in B1(X) and residue class rings of B1(X) modulo an ideal
• Mathematics
Applied General Topology
• 2019
<p>This paper explores the duality between ideals of the ring B<sub>1</sub>(X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called
On rings of Baire one functions
• Mathematics
Applied General Topology
• 2019
<p>This paper introduces the ring of all real valued Baire one functions, denoted by B<sub>1</sub>(X) and also the ring of all real valued bounded Baire one functions, denoted by
Spaces in which every dense subset is a Gδ
• Mathematics
• 2016
Abstract A topological space X is called a DGδ-space if every subset of X is a Gδ-set in its closure. In this paper we study DGδ-spaces that contains subspaces in which every dense subset is open and
On the maximal spectrum of commutative semiprimitive rings
The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The
An algebraic characterization of Blumberg spaces
Click on the link to view the abstract. Keywords: Without isolated point; almost discrete space; irresolvable space; openhereditarily irresolvable space; semiprime ring; Blumberg space Quaestiones
and A
• Taherifar, On the rings of functions which are discontinuous on a finite set, Houston J. Math. 44, no. 2
• 2018
On the rings of functions which are discontinuous on a finite set
• Houston J. Math
• 2018