Research Article

Uniformly graded-coherent rings

Published in: Quaestiones Mathematicae
Volume 44 , issue 10 , 2021 , pages: 1371–1391

DOI: 10.2989/16073606.2020.1799106

Author(s): Chahrazade Bakkari , Morocco , Najib Mahdou , Morocco , Abdelkbir Riffi , Morocco

Keywords: 13A02 , 13A15 , 13A02 , 13A15

Abstract

Let be a ring graded by an arbitrary grading abelian group Γ. We say that R is a uniformly graded-coherent ring if there is a map ϕ : ℕ → ℕ such that for every n ∈ ℕ, and any nonzero graded R-module homomorphism of degree 0, where λ ₁ , … ,λ_n are degrees in Γ, ker f can be generated by ϕ(n) homogeneous elements. In this paper, we provide the elementary properties of uniformly graded-coherent rings.

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