Finite rings in which commutativity is transitive
نویسندگان
چکیده
منابع مشابه
Groups in Which Commutativity Is a Transitive Relation
We investigate the structure of groups in which commutativity is a transitive relation on non-identity elements (CT-groups). A detailed study of locally nite, polycyclic, and torsion-free solvable CT-groups is carried out. Other topics include xed-point-free groups of automorphisms of abelian tor-sion groups and their cohomology groups.
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Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...
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We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...
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In this paper, we use the structure theory to prove an analog to a well-known theorem of Herstein as follows: Let R be a ring with center C such that for all x,y ? R either [x,y]= 0 or x-x [x,y]? C for some non negative integer n= n(x,y) dependingon x and y. Then R is commutative.
متن کاملGeneralized J-Rings and Commutativity
A J-ring is a ring R with the property that for every x in R there exists an integer n(x)>1 such that x x x n = ) ( , and a well-known theorem of Jacobson states that a Jring is necessarily commutative. With this as motivation, we define a generalized Jring to be a ring R with the property that for all x, y in R0 there exists integers 1 ) ( , 1 ) ( > = > = y m m x n n such that m n xy y x − is ...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2009
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-009-0142-y