This article is cited in 1 paper

Algebraic sets with fully characteristic radicals

Mohammad Shahryari

Faculty of Mathematical Sciences, University of Tabriz, 29 Bahman Blvd, Tabriz, 5166616471, Iran

Abstract: We obtain a necessary and sufficient condition for an algebraic set in a group to have a fully characteristic radical. As a result, we see that if the radical of a system of equation $S$ over a group $G$ is fully characteristic, then there exists a class $\mathfrak{X}$ of subgroups of $G$ such that elements of $S$ are identities of $\mathfrak{X}$.

Keywords: algebraic structures, equations, algebraic set, radical ideal, fully invariant congruence, fully characteristic subgroup.

UDC: 519.21

Received: 26.10.2016
Received in revised form: 26.11.2016
Accepted: 06.03.2017

Language: English

DOI: 10.17516/1997-1397-2017-10-3-293-297

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