# Common properties of some function rings on a topological space

@inproceedings{Zand2021CommonPO, title={Common properties of some function rings on a topological space}, author={Mohammad Reza Ahmadi Zand}, 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

- MathematicsApplied 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

- MathematicsApplied 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

- Mathematics
- 2000

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

- Mathematics
- 2010

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