Rings of functions which are discontinuous on a finite set with countable range

Achintya Singha; D. Mandal; Samir Ch Manda; Sagarmoy Bag

Rings of functions which are discontinuous on a finite set with countable range

General Topology 2023-10-04 v1

Authors: Achintya Singha , D. Mandal , Samir Ch Manda , Sagarmoy Bag

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 $C_c(X)_F$ .

Keywords

rings of functions discontinuous functions finite set countable range z-filters z-ideals baer ring zero divisor graph

Cite

@article{arxiv.2310.02010,
  title  = {Rings of functions which are discontinuous on a finite set with countable range},
  author = {Achintya Singha and D. Mandal and Samir Ch Manda and Sagarmoy Bag},
  journal= {arXiv preprint arXiv:2310.02010},
  year   = {2023}
}

Comments

19 pages. arXiv admin note: text overlap with arXiv:2109.06414

Rings of functions which are discontinuous on a finite set with countable range

Abstract

Keywords

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