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

DOI:
https://doi.org/10.1090/S0002-9939-1989-0943793-2

MathSciNet review:
943793

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper provides a proof of the following statement: Given a semiprimary ring , there is a quasi-hereditary ring and an idempotent such that .

**[A]**M. Auslander,*Representation dimension of Artin algebras*, Queen Mary College Mathematical Notes, (London), 1971.**[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****[DR ]**V. Dlab and C. M. Ringel,*Quasi-hereditary algebras*, Ill. J. Math. (to appear).**[DR ]**-,*Auslander algebras as quasi-hereditary algebras*, J. London Math. Soc. (to appear).**[PS]**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).**[S]**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A46,
16A65

Retrieve articles in all journals with MSC: 16A46, 16A65

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0943793-2

Article copyright:
© Copyright 1989
American Mathematical Society