ABELIAN EXACT SUBCATEGORIES CLOSED UNDER PREDECESSORS

ABSTRACT

In the category of finitely generated modules over an artinian ring, we classify all the abelian exact subcategories closed under predecessors or, equivalently, all the split torsion pairs with torsion-free class closed under quotients. In the context of artin algebras, the result is then applied to the left part of the module category and to local extensions of hereditary algebras.

Key Words:

• Abelian exact subcategories
• Closed under predecessors
• Hereditary injective modules
• Split torsion-free classes

Mathematical Subject Classification:

• 16G10
• 16P20
• 16E10

ACKNOWLEDGMENTS

The first author gratefully acknowledges partial support from the Natural Sciences and Engineering Research Council of Canada. The second author thanks the D.G.I. of the Spanish Ministry of Science and Technology and the Fundación “Séneca Direción General de Investigación” of Murcia for their financial support.

Notes

^#Communicated by Miguel Ferrero.

^†Dedicated to Claus M. Ringel on the occasion of his 60th birthday.