Monomial Algebras over Infinite Quivers. Applications to N-Complexes of Modules

Abstract

We apply previous techniques on infinite quivers to describe projective and injective modules over a monomial algebra Λ = RQ/I (where R is any arbitrary ring with identity). Then we consider the case and I is generated by paths of length N ≥ 2, so we get the category of so-called “N-complexes of R-modules”. For this category we will prove that if R has finite Gorenstein global dimension, then it is a Gorenstein category.

Key Words:

• Gorenstein category
• Monomial algebra
• N-complex

1991 Mathematics Subject Classification:

• Primary 18F20, 16G20, 20F38
• Secondary 16B50, 14F45

ACKNOWLEDGMENTS

The author is partially supported by the DGI MTM2005-0322. Estrada's research was supported by a MEC/Fulbright grant from the Spanish Secretaría de Estado de Universidades e Investigación del Ministerio de Educación y Ciencia.