Complements to Projective Almost Complete Tilting Modules

ABSTRACT

An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules.

Key Words:

• Complement
• Monomial algebras
• Tilting modules

Mathematics Subject Classification:

• 16G10

ACKNOWLEDGMENT

I would like to thank Prof. Idun Reiten for having introduced me to these problems and for her helpful comments and advice. A special thank to the algebra group of the Department of Mathematical Sciences at NTNU University for their kind hospitality during my stay in Trondheim, when part of this work was prepared.

Notes

^#Communicated by A. Facchini.