On The Number of Simple and Projective Modules in the Quasi-Tubes of Self-Injective Algebras

Abstract

We establish a bound on the number of simple and projective modules in the quasi-tubes of the Auslander–Reiten quivers of finite dimensional self-injective algebras over a field.

Key Words:

• Auslander–Reiten quiver
• Quasi-tube
• Self-injective algebra

2000 Mathematics Subject Classification:

• Primary: 16D50
• 16G70
• Secondary: 16G10

ACKNOWLEDGMENTS

The authors gratefully acknowledge support from the research grant No. N~N201 269 135 of the Polish Ministry of Science and Higher Education.

Notes

Communicated by D. Zacharia.