In this paper, we introduce the concept of the cohomological dimension filtration with respect to a system of ideals. In particular, a characterization of cohomological dimension filtration of a module by the associated prime ideals of its factors is established. As a main result, we provide a necessary and sufficient condition for an ascending chain of submodules of an $\mathfrak{R}$ -module $M$ to be the $\mathrm{cd}$-filtration of $M$, with respect to a system of ideals.
Faramarzi, S. O., & Valadbeigi, H. (2024). On the CD-filtration of modules with respect to a system of ideals. Journal of Algebra and Related Topics, 12(1), 127-136. doi: 10.22124/jart.2024.24405.1519
MLA
S. O. Faramarzi; H. Valadbeigi. "On the CD-filtration of modules with respect to a system of ideals". Journal of Algebra and Related Topics, 12, 1, 2024, 127-136. doi: 10.22124/jart.2024.24405.1519
HARVARD
Faramarzi, S. O., Valadbeigi, H. (2024). 'On the CD-filtration of modules with respect to a system of ideals', Journal of Algebra and Related Topics, 12(1), pp. 127-136. doi: 10.22124/jart.2024.24405.1519
VANCOUVER
Faramarzi, S. O., Valadbeigi, H. On the CD-filtration of modules with respect to a system of ideals. Journal of Algebra and Related Topics, 2024; 12(1): 127-136. doi: 10.22124/jart.2024.24405.1519
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