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Radicals of algebras graded by cancellative
linear semigroups

Author: A. V. Kelarev
Journal: Proc. Amer. Math. Soc. 124 (1996), 61-65
MSC (1991): Primary 16N20; Secondary 16S35
MathSciNet review: 1291778
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Abstract: We consider algebras over a field of characteristic zero, and prove that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup. It follows that the semigroup algebra of every linear cancellative semigroup is semisimple.

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  • 1 S. A. Amitsur, On the semisimplicity of group algebras, Michigan Math. J. 6 (1959), 251--253.MR 21:7256
  • 2 V. P. Camillo and K. R. Fuller, On graded rings with finiteness conditions, Proc. Amer. Math. Soc. 86 (1982), 1--6.MR 83h:16001
  • 3 M. V. Clase and A. V. Kelarev, Homogeneity of the Jacobson radical of semigroup graded rings, Comm. Algebra 22 (1994), 4963--4975.MR 95g:16044
  • 4 M. V. Clase, E. Jespers, A. V. Kelarev, and J. Okninski, Artinian semigroup graded rings, Bull. London Math. Soc. (to appear).
  • 5 E. Jespers, Radicals of graded rings, Theory of Radicals (Szekszárd, 1991), Colloq. Math. Soc. János Bolyai, vol. 61, North-Holland, Amsterdam and New York, 1993, pp. 109--130.MR 95d:16025
  • 6 E. Jespers and J. Okninski, Descending chain conditions and graded rings J. Algebra (to appear).
  • 7 G. Karpilovsky, The Jacobson radical of classical rings, Longman Sci. Tech., Harlow, 1991. MR 93a:16001
  • 8 A. V. Kelarev, A general approach to the structure of radicals in some ring constructions, Theory of Radicals (Szekszárd, 1991), Colloq. Math. Soc. János Bolyai, vol. 61, North-Holland, Amsterdam and New York, 1993, pp. 131--144.MR 94k:16036
  • 9 ------, On set graded rings, University of Stellenbosch, Department of Mathematics, Technical Report No. 10, 1993.
  • 10 L. G. Kovács, Semigroup algebras of the full matrix semigroup over a finite field, Proc. Amer. Math. Soc. 116 (1992), 911--920.MR 93b:16051
  • 11 J. Okninski, Semigroup algebras, Marcel Dekker, New York, 1991.MR 92f:20076
  • 12 J. Okninski and M. S. Putcha, PI semigroup algebras of linear semigroups, Proc. Amer. Math. Soc. 109 (1990), 39--46.MR 90j:20137
  • 13 ------, Complex representations of matrix semigroups, Trans. Amer. Math. Soc. 323 (1991), 563--581.MR 91e:20047
  • 14 ------, Semigroup algebras of linear semigroups, J. Algebra 152 (1992), 304--321.MR 93i:20081
  • 15 D. S. Passman, Radicals of twisted group rings. II, Proc. London Math. Soc. 22 (1971), 633--651.MR 45:2041
  • 16 ------, The algebraic structure of group rings, Wiley, New York, 1977.MR 81d:16001
  • 17 ------, Infinite crossed products and group-graded rings, Trans. Amer. Math. Soc. 284 (1984), 707--727.MR 85j:16012
  • 18 M. S. Putcha, Linear algebraic monoids, Cambridge Univ. Press, Cambridge, 1988.MR 90a:20003
  • 19 A. Reid, Twisted group algebras which are Artinian, perfect or self-injective, Bull. London Math. Soc. 7 (1975), 166--170.MR 52:475
  • 20 M. Saorín, Descending chain conditions for graded rings, Proc. Amer. Math. Soc. 115 (1992), 295--301.MR 92i:16032

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Additional Information

A. V. Kelarev

Received by editor(s): March 29, 1994
Received by editor(s) in revised form: August 12, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society

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