Rings of functions which are discontinuous on a finite set with countable range
| Autor: | Singha, Achintya, Mandal, D., Manda, Samir Ch, Bag, Sagarmoy |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $C_c(X)_F$. Comment: 19 pages. arXiv admin note: text overlap with arXiv:2109.06414 |
| Databáze: | arXiv |
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