|
This article is cited in 3 scientific papers (total in 3 papers)
Mathematical logic, algebra and number theory
On variety $\mathcal{N}$ of normal valued $m$-groups
A. V. Zenkova, O. V. Isaevab a Altai State Agricultural University, 98, Krasnoarmeysky ave., Barnaul, 656049, Russia
b Altai State University, 68, Socialistichesky ave., Barnaul, 656099, Russia
Abstract:
Recall that an $m$-group is a pair $(G,_{*}),$ where $G$ is an $\ell$-group and $_{*}$ is a decreasing order two automorphism of $G$. An $m$-group can be regarded as an algebraic system of signature $m$ and it is obvious that the $m$-groups form a variety in this signature. The set $M$ of varieties of all $m$-groups is a partially ordered set with respect to the set-theoretic inclusion. Moreover, $M$ is a lattice with respect to the naturally defined operations of intersection and union of varieties of $m$-groups. In this article we study the characteristics of a variety $\mathcal{N}$ of normal valued $m$-groups which is defined by the identity $ |x||y|\wedge |y|^{2}|x|^{2}=|x||y|.$ We will prove that $\mathcal{N}$ is an idempotent of $M$ and $\mathcal{N}=\bigvee\limits_{n \in \mathbb{N}}\mathcal{A}^{n},$ where $\mathcal{A}$ is the variety of all abelian $m$-groups.
Keywords:
$m$-group, variety, normal valued $m$-group.
Received October 18, 2020, published February 3, 2021
Citation:
A. V. Zenkov, O. V. Isaeva, “On variety $\mathcal{N}$ of normal valued $m$-groups”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 54–60
Linking options:
https://www.mathnet.ru/eng/semr1346 https://www.mathnet.ru/eng/semr/v18/i1/p54
|
Statistics & downloads: |
Abstract page: | 182 | Full-text PDF : | 72 | References: | 10 |
|