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Rings of functions which are discontinuous on a finite set with countable range
- Publication Year :
- 2023
-
Abstract
- Consider the ring $C_c(X)_F$ of real valued functions which are discontinuous on a finite set with countable range. We discuss $(\mathcal{Z}_c)_F$-filters on $X$ and $(\mathcal{Z}_c)_F$-ideals of $C_c(X)_F$. We establish an analogous version of Gelfand-Kolmogoroff theorem in our setting. We prove some equivalent conditions when $C_c(X)_F$ is a Baer-ring and a regular ring. Lastly, we talk about the zero divisor graph on $C_c(X)_F$.<br />Comment: 19 pages. arXiv admin note: text overlap with arXiv:2109.06414
- Subjects :
- Mathematics - General Topology
54C30 (Primary), 54C40 (Secondary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2310.02010
- Document Type :
- Working Paper