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

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

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arXiv · 2310.02010

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

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

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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 $C_c(X)_F$.

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BibTeX RIS

Achintya Singha, D. Mandal, Samir Ch Manda, Sagarmoy Bag. 2023-10-03. Rings of functions which are discontinuous on a finite set with countable range. https://arxiv.org/abs/2310.02010

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