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Characterization of rings by some filters | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، S1، تیر 2026، صفحه 81-87 اصل مقاله (145.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.27636.1676 | ||
| نویسندگان | ||
| H. Mouadi1؛ A. Boua* 2 | ||
| 1Department of Mathematics and Informatics, University Ibn Zohr, Polydisciplinary Faculty, Lisima, Taroudant, Morocco | ||
| 2Department of Mathematics, University Sidi Mohammed Ben Abdellah-Fez, Polydisciplinary Faculty, Taza, Morocco | ||
| چکیده | ||
| Let $R=\prod_{i\in I}R_{i}$ be the product of an infinite family of rings $\{R_{i}\}_{i\in I}$. In this study, we investigate the direct sum $\bigoplus_{i\in I}R_{i}$. Special attention is paid to the relationship between the ideal $\bigoplus_{i\in I}R_{i}$ and the $\mathcal{F}_{r}$ Frechet filter in $I$, also we show a new characterization of $\bigoplus_{i\in I}R_{i}$ by the $\mathcal{F}_{r}-\lim$. | ||
| کلیدواژهها | ||
| Direct product؛ Direct sum؛ Frechet filter؛ $\mathcal{F}_{r}-\lim$ | ||
| مراجع | ||
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[1] S. Garcia-Ferreira and L. M. Ruza-Montilla, The F − lim of a sequence of prime ideals, Communications in Algebra, 39 (2011), 2532–2544. [2] S. Garcia-Ferreira and H. S. Pino-Villela, Characterizing filters by convergence (with respect to filters) in Banach spaces, Topology and its Applications, (4) 159 (2012), 1246–1257. [3] S. García-Ferreira and J. E. Rivera-Gómez, Comparing Fréchet-Urysohn filters with two preorders, Topology and its Applications, 225 (2017), 90-102. [4] S. García-Ferreira and J. E. Rivera-Gómez, Ordering Fréchet-Urysohn filters, Topology and its Applications, 163 (2014), 128-141. [5] R. Gilmer, Zero-dimensional extension rings and subrings, zero-dimensional commutative rings, zero-dimensional rings, Lecture Note in Pure and Applied Mathematics, 171 (1995), 27–39. [6] R. Gilmer and W. Heinzer, Product of commutative rings and zero-dimensionality, Transactions of the American Mathematical Society, 331 (1992), 663–680. [7] H. Mouadi and D. Karim, Characterization of prime and maximal ideals of product rings by F − lim, Kyungpook Mathematical Journal, (4) 61 (2021), 823–830. | ||
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آمار تعداد مشاهده مقاله: 324 تعداد دریافت فایل اصل مقاله: 213 |
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