Abstract
Let R he a nil ring with bounded index. It is known that the ring of polynomials R[t] is nil with hounded index, and a bound for its index can be given. This is used to get a bound for the index of the matrix ring Mk(R). If R is not necessarily nil hut has hounded index and satisfies a multilinear monic identity, then Mk(R)has hounded index, and a hound for Its index is given.
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Beferences
Jacobson, N., “Shirshov’s theorem on local finiteness”, 1978, Lecture Notes in Math. Springer Verlag 697, pp. 25–46.
Klein, A.A., “Bings with hounded index of nilpotence”, 1982, Contemporary Math. 13, pp. 151 - 154.
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© 1984 D. Reidel Publishing Company
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Klein, A.A. (1984). The Index of Nility of a Matrix Ring over a Ring with Bounded Index. In: van Oystaeyen, F. (eds) Methods in Ring Theory. NATO ASI Series, vol 129. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6369-6_16
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DOI: https://doi.org/10.1007/978-94-009-6369-6_16
Publisher Name: Springer, Dordrecht
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