On the adjoint group of some radical rings

Author:

Dickenschied Oliver

Abstract

A ring R is called radical if it coincides with its Jacobson radical, which means that Rforms a group under the operation a ° b = a + b + ab for all a and b in R. This group is called the adjoint group R° of R. The relation between the adjoint group and the additive group R+ of a radical rin R is an interesting topic to study. It has been shown in [1] that the finiteness conditions “minimax”, “finite Prufer rank”, “finite abelian subgroup rank” and “finite torsionfree rank” carry over from the adjoint group to the additive group of a radical ring. The converse is true for the minimax condition, while it fails for all the other above finiteness conditions by an example due to Sysak [6] (see also [2, Theorem 6.1.2]). However, we will show that the converse holds if we restrict to the class of nil rings, i.e. the rings R such that for any a є R there exists an n = n(a) with an = 0.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Adjoint groups of $p$-nil rings and $p$-group automorphisms;Bulletin of the Belgian Mathematical Society - Simon Stevin;2014-05-01

2. Radical Rings with Engel Conditions;Journal of Algebra;2000-09

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