Multi-groups

被引：1

作者：

Kozlovskaya, Tatyana A. ^{[1
]}

机构：

[1] Tomsk State Univ, Reg Sci & Educ Math Ctr, Tomsk, Russia

来源：

VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS | 2024年 / 87期

关键词：

algebraic system; homogeneous algebraic system; groupoid; semigroup; monoid; group; semigroup system; quandle system; dimonoid; skew brace; multi-group; multi-quandle; ALGEBRAS; RINGS;

D O I：

10.17223/19988621/87/4

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In the present paper we define homogeneous algebraic systems. Particular cases of these systems are semigroup (monoid, group) systems. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, and N. Koreshkov. Quandle systems were introduced and studied by V. Bardakov, D. Fedoseev, and V. Turaev. We construct some group systems on the set of square matrices over a field k. Also, we define rack systems on the set V x G, where V is a vector space of dimension n over and G is a subgroup of GL(n)(k) nGL. Finally, we find the connection between skew braces and dimonoids.

引用

页码：34 / 43

页数：10

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