2017-05-04

# Involution satisfying a local Engel or power commuting condition

## Publication

### Publication

*Communications in Algebra , Volume 45 - Issue 5 p. 2018- 2028*

We are given a semiprime PI-ring R (i.e. R satisfies some polynomial identity) with *. It is to be shown that the following conditions are equivalent. Condition 1: Each element x of R is normal (i.e. (Formula presented.)). Condition 2: Associated to each element x of R is a natural number N = N(x) depending on x such that (Formula presented.) where dx maps each element y of R onto [y,x](= yx−xy) and (Formula presented.) is the Nth power of dx (under composition). Condition 3: * Associated to each element x of R is a natural number (Formula presented.) depending on x such that (Formula presented.).

Additional Metadata | |
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Keywords | Local Engel condition, local power commuting condition, ring with involution, semiprime ring |

Persistent URL | dx.doi.org/10.1080/00927872.2016.1226879 |

Journal | Communications in Algebra |

Citation |
Chacron, M. (2017). Involution satisfying a local Engel or power commuting condition.
Communications in Algebra, 45(5), 2018–2028. doi:10.1080/00927872.2016.1226879 |