Weakly uniformly graded-coherent rings
Abdelkbir Riffi
Laboratory of Mathematics and applications (LMA), Department of Mathematics,
Faculty of Sciences, Ibn Zohr University, Agadir, Morocco.
Pages 219-231 | Received 20 October 2023, Accepted 17 January 2024, Published 30 June 2024
Abstract
Let R=\bigoplus_{\alpha\in\Gamma}R_\alpha be a ring graded by an arbitrary grading abelian group \Gamma. We say that R is a weakly uniformly graded-coherent ring if there is a map \phi:\mathbb{N}\rightarrow\mathbb{N} such that for every n\in\mathbb{N}, and any nonzero graded R-module homomorphism f:\bigoplus_{i=1}^{n}R(-\lambda_{i})\rightarrow R of degree 0, where \lambda_{1},\ldots,\lambda_{n} are degrees in \Gamma,\ ker\,f can be generated by \phi(n) elements (not necessary homogeneous). In this paper, we provide the elementary properties of weakly uniformly graded-coherent rings.
Keywords: Weakly uniformly graded-coherent, uniformly graded-coherent, graded-coherent, uniformly coherent, coherent, graded modules and rings.
MSC numbers: 13A02, 13A15.
Downloads: Full-text PDF