Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Examples of ungradable algebras


Authors: Th. Belzner, W. D. Burgess, K. R. Fuller and R. Schulz
Journal: Proc. Amer. Math. Soc. 114 (1992), 1-4
MSC: Primary 16P10; Secondary 16W50
DOI: https://doi.org/10.1090/S0002-9939-1992-1062382-5
MathSciNet review: 1062382
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Examples are presented of finite-dimensional algebras that admit no positive grading (that is, a nontrivial grading indexed by the natural numbers). Some of these examples have finite global dimension (they are even quasihereditary), and yield a negative answer to a question of Anick and Green.


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

  • [1] D. J. Anick and E. L. Green, On the homology of quotients of path algebras, Comm. Algebra 15 (1987), 309-342. MR 876982 (88c:16033)
  • [2] M. Auslander, Representation theory of artin algebras II, Comm. Algebra 1 (1974), 177-268. MR 0349747 (50:2240)
  • [3] V. P. Camillo and K. R. Fuller, On graded rings with finiteness conditions, Proc. Amer. Math. Soc. 86 (1982), 1-5. MR 663852 (83h:16001)
  • [4] E. Kline, B. Parshall, and L. Scott, Finite dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 277-291. MR 961165 (90d:18005)
  • [5] V. Dlab and C. M. Ringel, Quasihereditary algebras, Illinois J. Math. 33 (1989), 280-291. 1988. MR 987824 (90e:16023)
  • [6] -, Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring, Proc. Amer. Math Soc. 107 (1989), 1-5. MR 943793 (89m:16033)
  • [7] R. Gordon and E. L. Green, Graded artin algebras, J. Algebra 76 (1982), 111-137. MR 659212 (83m:16028a)
  • [8] R. S. Pierce, Associative algebras, Springer-Verlag, Berlin, Heidelberg, and New York, 1982. MR 674652 (84c:16001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16P10, 16W50

Retrieve articles in all journals with MSC: 16P10, 16W50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1062382-5
Keywords: Graded algebras, ungradable algebras, finite global dimension
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society