All tilting modules are of countable type | Zendy

Šťovíček Jan | Zendy; Trlifaj Jan | Zendy

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All tilting modules are of countable type

Author(s) -

Šťovíček Jan,

Trlifaj Jan

Publication year - 2007

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdl019

Subject(s) - countable set , mathematics , type (biology) , pure mathematics , dimension (graph theory) , class (philosophy) , projective test , resolution (logic) , set (abstract data type) , projective module , projective cover , ring (chemistry) , discrete mathematics , projective space , collineation , computer science , chemistry , organic chemistry , artificial intelligence , programming language , ecology , biology

Let R be a ring and T an (infinitely generated) tilting module. Then T is of countable type; that is, there is a set, , of modules possessing a projective resolution consisting of countably generated projective modules such that the tilting class T ⊥ equals ⊥ . Moreover, a cotorsion pair ℭ = (, ℬ) is tilting if and only if: ℭ is hereditary, all modules in have finite projective dimension, and ℬ is closed under arbitrary direct sums.

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