Rings of Quotients of Rings of Functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910751666470912 |
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| author | Fine, N. J. Gillman, L. Lambek, J. |
| author_facet | Fine, N. J. Gillman, L. Lambek, J. |
| contents | From the original PREFACE: The rings of quotients recently introduced by Johnson and Utumi are applied to the ring $C(X)$ of all continuous real-valued functions on a completely regular space $X$. Let $Q(X)$ denote the maximal ring of quotients of $C(X)$; then $Q(X)$ may be realized as the ring of all continuous functions on the dense open sets of $X$ (modulo an obvious equivalence relation). In special cases (e.g., for metric $X$), $Q(X)$ reduces to the classical ring of quotients of $C(X)$ (formed with respect to the regular elements), but in general, the classical ring is only a proper sub-ring of $Q(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rings of Quotients of Rings of Functions Fine, N. J. Gillman, L. Lambek, J. General Topology Rings and Algebras 46.55 (54.60) From the original PREFACE: The rings of quotients recently introduced by Johnson and Utumi are applied to the ring $C(X)$ of all continuous real-valued functions on a completely regular space $X$. Let $Q(X)$ denote the maximal ring of quotients of $C(X)$; then $Q(X)$ may be realized as the ring of all continuous functions on the dense open sets of $X$ (modulo an obvious equivalence relation). In special cases (e.g., for metric $X$), $Q(X)$ reduces to the classical ring of quotients of $C(X)$ (formed with respect to the regular elements), but in general, the classical ring is only a proper sub-ring of $Q(X)$. |
| title | Rings of Quotients of Rings of Functions |
| topic | General Topology Rings and Algebras 46.55 (54.60) |
| url | https://arxiv.org/abs/2403.04079 |