Abstract Using the Freese–McKenzie commutator theory for congruence modular varieties
as the starting point, we develop commutator theory for the variety of loops. The fundamental …

A perfect matroid design (PMD) is a matroid such that all flats of rank i have the same
cardinality a;. Some other names used for PMDs are: uniformly designed lattices, geometric …

arXiv:0811.3787v1 [math.RA] 24 Nov 2008 Commutative Moufang loops and alternative
algebras Page 1 arXiv:0811.3787v1 [math.RA] 24 Nov 2008 Commutative Moufang loops and …

Статья представляет собой обзор современного состояния теории неассоциативных
структур, близких к ассоциативным. Речь идет об йордановых и альтернативных …

This paper initiates a unified module theory for four varieties of quasigroups: semisymmetric,
semisymmetric idempotent, totally symmetric, and totally symmetric idempotent. These …

Two connexions between quasigroups and quandles are established. In one direction,
Joyce's homogeneous quandle construction is shown to yield a quasigroup isotopic to the …

1. Introduction. This paper is concerned with proving identities in commutative Moufang
loops. Many such identities were derived in chapter VIII of (1) in the course of demonstrating …

Цель: изучение структурной теории неассоциативных структур-теории радикалов луп,
луп обратимых элементов альтернативных луповых колец и Ω-луп. Приложения …

Аннотация В работе рассмотрены основные свойства коммутантов нормальных
подлуп заданной лупы. Предложено понятие первичного радикала для луп и дана его …

Let E be a given finitely generated Commutative Moufang Loop (CML for short); let k (E) be
its associative central nilpotency class, Φ (E) its Frattini subloop and Γ (E) the smallest …