Finite Higher Commutators in Associative Rings

Lanski, Charles

doi:10.1017/s0004972713000890

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2017

2022

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Cited by 2 publications

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“…H. Bell [5] has proved that if I is a nonzero right ideal of finite index in a prime ring R and OEI; I is finite, then R is either finite or commutative (see also [17,Corollary 1.2]). C. Lanski [16] has showed that if T is a finite higher commutator of R containing no nonzero nilpotent element, then T generates a finite ideal of R.…”

Section: Introductionmentioning

confidence: 99%

$FC$-rings

Artemovych¹

2017

MMN

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Abstract. We investigate properties of F C -rings (i.e. rings R in which the centralizer C R .a/ of any element a 2 R is of finite index in R) and, in particular, characterize left Artinian rings with a finite set of all derivations Der R (respectively inner derivations IDer R). We show that if R is a Jacobson radical ring in which its adjoint group R ı has a finite number of conjugacy classes, thenis a ring direct sum of Jacobson radical rings R p i and D, where the additive group D C is a torsion-free divisible group, the adjoint group D ı is a group with a finite number of conjugacy classes, R C p i is a finite p i -group .i D 1; : : : ; t/ and p 1 ; : : : ; p t are pairwise distinct primes.

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Section: Introductionmentioning

confidence: 99%