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A short note on the Schur-Jacobson theorem

Author: R. C. Cowsik
Journal: Proc. Amer. Math. Soc. 118 (1993), 675-676
MSC: Primary 13E10; Secondary 13C15
MathSciNet review: 1139475
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Abstract: An upper bound for the length of a commutative Artinian ring in terms of the length of a faithful module is given. This generalizes a theorem of Schur and Jacobson.

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

  • [1] W. H. Gustafson, On maximal commutative algebras of linear transformations, J. Algebra 42 (1976), 557-563. MR 0422341 (54:10331)
  • [2] N. Jacobson, Schur's Theorems on commutative matrices, Bull. Amer. Math. Soc. 50 (1946), 431-436. MR 0010540 (6:33b)
  • [3] I. Schur, Zur theorie vertauschbaren matrizen, Crelle's J. 130 (1905), 66-76.

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Article copyright: © Copyright 1993 American Mathematical Society

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