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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Homological theory of idempotent ideals


Authors: M. Auslander, M. I. Platzeck and G. Todorov
Journal: Trans. Amer. Math. Soc. 332 (1992), 667-692
MSC: Primary 16G10; Secondary 16D25, 16D90
DOI: https://doi.org/10.1090/S0002-9947-1992-1052903-5
MathSciNet review: 1052903
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Abstract: Let $ \Lambda $ be an artin algebra $ \mathfrak{A}$ and a two-sided ideal of $ \Lambda $. Then $ \mathfrak{A}$ is the trace of a projective $ \Lambda $-module $ P$ in $ \Lambda $. We study how the homological properties of the categories of finitely generated modules over the three rings $ \Lambda /\mathfrak{A}$, $ \Lambda $ and the endomorphism ring of $ P$ are related. We give some applications of the ideas developed in the paper to the study of quasi-hereditary algebras.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1052903-5
Keywords: idempotent ideal, projective resolution, quasihereditary algebra
Article copyright: © Copyright 1992 American Mathematical Society