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Weak u-s-projective modules and dimensions | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 1، مهر 2025، صفحه 173-188 اصل مقاله (187.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.24832.1545 | ||
| نویسندگان | ||
| R. A. Assaad* 1؛ X. Zhang2 | ||
| 1Department of Artificial Intelligence, Faculty of Computer Science & Information Technology, Al-Razi University, Sana'a, Yemen | ||
| 2School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China | ||
| چکیده | ||
| The primary focus of this paper is to introduce and investigate a fresh category of projective modules, referred to as weak $u$-$S$-projective modules ($w$-$u$-w-u- is an abbreviation for weak uniformly). These novel modules are utilized for characterizing $u$-$S$-von Neumann regular rings. Additionally, the paper investigates a new type of rings, named $u$-$S$-semihereditary rings. This leads to the introduction of the weak $u$-$S$-projective dimensions of modules and weak $u$-$S$-global dimension of rings in this paper. | ||
| کلیدواژه‌ها | ||
| $u$-$S$-projective module؛ $u$-$S$-torsion؛ $u$-$S$-exact sequence؛ $u$-$S$-von Neumann regular ring؛ $u$-$S$-semihereditary | ||
| مراجع | ||
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[1] D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra, 30 (2002), 4407-4416. [2] R. A. K. Assaad and X. Zhang, Weak u-S-flat modules and dimensions, Kyu. Math. J., 36 (2023), 333-344. [3] R. A. K. Assaad and X. Zhang, S-FI-flat and S-FI-injective modules, submitted. [4] D. Bennis and M. El Hajoui, On S-coherence, J. Korean Math. Soc., 55 (2018), 1499-1512. [5] W. Qi, H. Kim, F. G. Wang, M. Z. Chen and W. Zhao, Uniformly S-Noetherian rings, Quaestiones Mathematicae, (2022). [6] F. Wang and H. Kim, Foundations of commutative rings and their modules, Springer Nature Singapore Pte Ltd., Singapore, 2016. [7] F. Wang and L. Qiao, The w-weak global dimension of commutative rings, Bull. Korean Math. Soc., 52 (2015), 1327-1338. [8] X. L. Zhang, Characterizing S-flat modules and S-von Neumann regular rings by uniformity, Bull. Korean Math. Soc., (3) 59 (2022), 643-657. [9] X. L. Zhang, On uniformly S-absolutely pure modules, J. Korean Math. Soc., (3) 60 (2023), 521-536. [10] X. L. Zhang, The u-S-weak global dimension of commutative rings, Commun. Korean Math. Soc., (1) 38 (2023), 97-112. [11] X. L. Zhang and W. Qi, Characterizing S-projective modules and S-semisimple rings by uniformity, J. Commut. Algebra, (2021). [12] X. L. Zhang and W. Qi, The u-S-global dimensions of commutative rings, Bull. Korean Math. Soc., (6) 60 (2023), 1523-1537. [13] X. L. Zhang, On uniformly S-coherent rings, Rocky Mountain J. Math., to appear. | ||
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