On certain properties and invariants of graded rings and modules

TL;DR

This paper investigates how various properties and invariants of graded rings and modules behave under coarsening functors, including aspects like simplicity, reducedness, homological dimensions, and adjoint functors.

Contribution

It provides new insights into the behavior of graded ring and module properties under coarsening functors, extending understanding of homological and structural invariants.

Findings

Behavior of simple, entire, or reduced graded rings under coarsening is characterized.

Homological dimensions of graded modules are analyzed in the context of coarsening.

Adjoints of degree restriction functors are studied for their properties and applications.

Abstract

The behaviour under coarsening functors of simple, entire, or reduced graded rings, of free graded modules over principal graded rings, of superfluous monomorphisms and of homological dimensions of graded modules, as well as adjoints of degree restriction functors, are investigated.