Characterization of rings by some filters

Document Type : Research Paper

Authors

1 Department of Mathematics and Informatics, University Ibn Zohr, Polydisciplinary Faculty, Lisima, Taroudant, Morocco

2 Department of Mathematics, University Sidi Mohammed Ben Abdellah-Fez, Polydisciplinary Faculty, Taza, Morocco

Abstract

‎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 $\mathcal{F}_{r}-\lim$‎.

Keywords

Main Subjects

References

[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.

Files

Share

How to cite

Statistics