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Artinian rings with nilpotent adjoint group

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Abstract

Let R be an Artinian ring (not necessarily with unit element), let Z(R) be its center, and let R° be the group of invertible elements of the ring R with respect to the operation a ∘ b = a + b + ab. We prove that the adjoint group R° is nilpotent and the set Z(R) + R° generates R as a ring if and only if R is the direct sum of finitely many ideals each of which is either a nilpotent ring or a local ring with nilpotent multiplicative group.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    R. Yu. Evstaf’ev

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  1. R. Yu. Evstaf’ev
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 417–426, March, 2006.

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Evstaf’ev, R.Y. Artinian rings with nilpotent adjoint group. Ukr Math J 58, 472–481 (2006). https://doi.org/10.1007/s11253-006-0079-4

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  • DOI: https://doi.org/10.1007/s11253-006-0079-4

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