Geodesic
On the adjoint group of some radical rings
Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 35-41

Voir la notice de l'article provenant de la source Cambridge University Press

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 R° 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. 
Dickenschied, Oliver. On the adjoint group of some radical rings. Glasgow mathematical journal, Tome 39 (1997) no. 1, pp. 35-41. doi: 10.1017/S0017089500031888
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[1] 1.Amberg, B. and Dickenschied, O., On the adjoint group of a radical ring, Canad. Math. Bull. 38 (1995), 262–270. Google Scholar | DOI

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