Quasinilpotents in rings and their applications | Zendy

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Quasinilpotents in rings and their applications

Author(s) -

Jian Cui

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1706-79

Subject(s) - mathematics , ring (chemistry) , jacobson radical , invertible matrix , element (criminal law) , associative property , pure mathematics , reduced ring , set (abstract data type) , discrete mathematics , principal ideal ring , algebra over a field , law , commutative ring , computer science , chemistry , organic chemistry , commutative property , political science , programming language

An element a of an associative ring R is said to be quasinilpotent if 1 − ax is invertible for every x ∈ R with xa = ax . Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.

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