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

MathSciNet review:
1052903

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Abstract: Let be an artin algebra and a two-sided ideal of . Then is the trace of a projective -module in . We study how the homological properties of the categories of finitely generated modules over the three rings , and the endomorphism ring of are related. We give some applications of the ideas developed in the paper to the study of quasi-hereditary algebras.

**[A]**Maurice Auslander,*Representation theory of Artin algebras. I, II*, Comm. Algebra**1**(1974), 177–268; ibid. 1 (1974), 269–310. MR**0349747****[BF]**W. D. Burguess and K. R. Fuller,*On quasihereditary rings*, 1988 (preprint).**[CE]**Henri Cartan and Samuel Eilenberg,*Homological algebra*, Princeton University Press, Princeton, N. J., 1956. MR**0077480****[CPS]**E. Cline, B. Parshall, and L. Scott,*Finite-dimensional algebras and highest weight categories*, J. Reine Angew. Math.**391**(1988), 85–99. MR**961165****[DR1]**Vlastimil Dlab and Claus Michael Ringel,*Quasi-hereditary algebras*, Illinois J. Math.**33**(1989), no. 2, 280–291. MR**987824****[DR2]**-,*Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring*, 1987 (preprint).**[PS]**B. Parshall and L. Scott (Eds.),*Derived categories, quasihereditary algebras and algebraic groups*, Proc. Ottawa-Mosonee Workshop in Algebra, Math. Lecture Notes Series No. 3, Center for Research in Algebra and Related Topics.

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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