Injective Covers and Envelopes of Representations of Linear Quivers

Abstract

It is known that for a ring R every left R-module has an injective cover if and only if R is left Noetherian. For a quiver Q and a ring R it is also known that the category (Q, R − Mod) of representations of Q by left R-modules is such that every object has an injective cover if R is Noetherian and Q is a Noetherian quiver. In this article, we will initiate a study of these injective covers by describing them for the line quivers A _n and A _∞ ⁺.

Key Words:

• Injective cover
• Injective envelope
• Representation of a quiver

2000 Mathematics Subject Classification:

• 16G20
• 16B50

ACKNOWLEDGMENT

This article was supported by Dong-A University Research Fund, in 2007.

Notes

Communicated by J. L. Gomez Pardo.