Prime Radical of Loops and Ω-Loops. I

A. V. Gribov; A. V. Mikhalev

doi:10.1007/s10958-016-2707-3

Prime Radical of Loops and Ω-Loops. I

Authors: Gribov A.V.¹, Mikhalev A.V.¹
Affiliations:
1. Moscow State University
Issue: Vol 213, No 2 (2016)
Pages: 145-157
Section: Article
URL: https://journals.rcsi.science/1072-3374/article/view/237146
DOI: https://doi.org/10.1007/s10958-016-2707-3
ID: 237146

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Abstract

In this paper, main properties of a commutator of two normal subloops of a loop are considered. The notion of a prime radical of loops is introduced and its characterization as a set of strongly Engel elements is given. Also an Ω-prime radical of Ω-loops is defined and its elementwise characterization is given.

Keywords

Prime Radical, Universal Algebra, Normal Closure, Additive Loop, Prime Loop

About the authors

A. V. Gribov

Moscow State University

Author for correspondence.
Email: alexey.gribov@yandex.ru
Russian Federation, Moscow

A. V. Mikhalev

Moscow State University

Email: alexey.gribov@yandex.ru
Russian Federation, Moscow

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