Uniformly graded-coherent rings

Commutative graded-$n$-coherent and graded valuation rings

“…Section 2 begins, more generally, by defining graded-n-coherent modules for each integer n ≥ 1. As one might expect, the graded-1-coherent modules are just the "graded-coherent modules" in [2]. Among other things, we show that, if R is a graded ring and…”

“…Obviously, every n-coherent graded ring is a graded-n-coherent ring. The converse is not true in general, example 3.2 in [2] gives an example of graded-1-coherent ring which is not 1-coherent.…”

“…It follows from [2] that the graded-1-coherent modules are just the "graded-coherent modules". Remark 2.2.…”

“…The concept of coherence has many graded generalizations, see e.g.,( [2] and [3]). Among these generalizations, we have the graded-n-coherence.…”