Noncommutative higher commutators

EROĞLU M. P.

JOURNAL OF ALGEBRA, cilt.594, ss.101-108, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 594
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.jalgebra.2021.11.034
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.101-108
  • Anahtar Kelimeler: Lie structure, Commutator, Higher commutator, Lie ideal, Noncommutative algebra, Semiprime algebra, IDEALS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let A be a unital algebra over a field of characteristic different from 2. The main goal of this work is to characterize higher commutators of A. In particular, we show that if H is a noncommutative higher commutator of A and contains the unity, then H is equal to either A or [A, A]. As a result, we prove that if there exist x, y is an element of A such that 1 = [x, y], then the only higher commutators of A are A and [A, A]. We also consider the structure of noncommutative Lie ideals of the form [U, A], where U is a Lie ideal of A, and show that if L = [U, A] is noncommutative and contains the unity, then L = [A, A] and [A, A] subset of U.(c) 2021 Published by Elsevier Inc.