Homological theory of idempotent ideals
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- by M. Auslander, M. I. Platzeck and G. Todorov PDF
- Trans. Amer. Math. Soc. 332 (1992), 667-692 Request permission
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.References
- Maurice Auslander, Representation theory of Artin algebras. I, II, Comm. Algebra 1 (1974), 177–268; ibid. 1 (1974), 269–310. MR 349747, DOI 10.1080/00927877408548230 W. D. Burguess and K. R. Fuller, On quasihereditary rings, 1988 (preprint).
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- E. Cline, B. Parshall, and L. Scott, Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85–99. MR 961165
- Vlastimil Dlab and Claus Michael Ringel, Quasi-hereditary algebras, Illinois J. Math. 33 (1989), no. 2, 280–291. MR 987824 —, Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring, 1987 (preprint). 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.
Additional Information
- © Copyright 1992 American Mathematical Society
- 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