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Proceedings of the American Mathematical Society

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Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring

Authors: Vlastimil Dlab and Claus Michael Ringel
Journal: Proc. Amer. Math. Soc. 107 (1989), 1-5
MSC: Primary 16A46; Secondary 16A65
MathSciNet review: 943793
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Abstract: The paper provides a proof of the following statement: Given a semiprimary ring $R$, there is a quasi-hereditary ring $A$ and an idempotent $e \in A$ such that $R \simeq eAe$.

References [Enhancements On Off] (What's this?)

    M. Auslander, Representation dimension of Artin algebras, Queen Mary College Mathematical Notes, (London), 1971.
  • E. Cline, B. Parshall, and L. Scott, Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85–99. MR 961165
  • V. Dlab and C. M. Ringel, Quasi-hereditary algebras, Ill. J. Math. (to appear). ---, Auslander algebras as quasi-hereditary algebras, J. London Math. Soc. (to appear). B. Parshall and L. Scott, Derived categories, quasi-hereditary algebras and algebraic groups, Proc. Ottawa-Moosonee Workshop in Algebra, Carleton Univ. Notes No. 3 (1988).
  • Leonard L. Scott, Simulating algebraic geometry with algebra. I. The algebraic theory of derived categories, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 271–281. MR 933417

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Article copyright: © Copyright 1989 American Mathematical Society