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Torsion Theories Induced by Tilting Modules

Published online by Cambridge University Press:  20 November 2018

Ibrahim Assem
Ibrahim Assem*
Affiliation:
University of Ottawa, Ottawa, Ontario
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Let k be a commutative field, and A a finite-dimensional k-algebra. By a module will always be meant a finitely generated right module. Following [8], we shall call a module TA a tilting module if (1) pdTA ≦ 1, (2) Ext1A(T, T) = 0 and (3) there is a short exact sequence

with T’ and T” direct sums of direct summands of T. Given a tilting module TA, the full subcategories

and

of the category modA of A -modules are respectively the torsion-free class and the torsion class of a torsion theory on modA[8]. The aim of the present paper is to find conditions on a torsion theory in order that it be induced by a tilting module.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 5 , 01 October 1984 , pp. 899 - 913
Copyright
Copyright © Canadian Mathematical Society 1984

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