The radical of a module category of string algebra

ABSTRACT

We study how to read from the ordinary quiver of a representation-finite string algebra, the minimal lower bound m ≥ 1 such that the mth power of the radical of its module category vanishes. We also show how to read the degree of any irreducible morphism in such a representation-finite string algebras considering strings.

KEYWORDS:

• Degrees
• irreducible morphisms
• radical
• string algebras

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 16G70
• 16G20
• 16E10

Acknowledgment

Both authors thankfully acknowledge partial support from CONICET and from Universidad Nacional de Mar del Plata, Argentina. The results of this article are part of the Ph.D.’s thesis of the second author under the supervision of the first one. The first author is a researcher from CONICET. We also would like to thank the referee for his/her questions which helped to improve the paper.