The commingling of commutativity and associativity in Bol loops

Commentationes mathematicae Universitatis Carolinae

J. D. Phillips¹ 

关键词: Bol;    Moufang;    loop;    commutant;    associator;   

DOI  :  10.14712/1213-7243.2015.185

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Commutative Moufang loops were amongst the first (nonassociative) loops to be investigated; a great deal is known about their structure. More generally, the interplay of commutativity and associativity in (not necessarily commutative) Moufang loops is well known, e.g., the many associator identities and inner mapping identities involving commutant elements, especially those involving the exponent three. Here, we investigate all of this in the variety of Bol loops.

【 授权许可】

CC BY