2017
Том 69
№ 6

All Issues

Artinian rings with nilpotent adjoint group

Evstaf’ev R. Yu.

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Abstract

Let $R$ be an Artinian ring (not necessarily with unit element), let $Z(R)$ be its center, and let $R ^{\circ}$ 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 $R ^{\circ}$ is nilpotent and the set $Z (R) + R ^{\circ}$ 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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 3, pp 472-481.

Citation Example: Evstaf’ev R. Yu. Artinian rings with nilpotent adjoint group // Ukr. Mat. Zh. - 2006. - 58, № 3. - pp. 417–426.

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