Geodesic
Right Bol Quasi-Fields
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1409-1420

Voir la notice de l'article provenant de la source Cambridge University Press

We shall consider quasi-fields which satisfy the multiplicative Identity 1.1 (1.1) will be called the right Bol law and a quasi-field satisfying it will be called a right Bol quasi-held. Moufang quasi-fields, i.e., those satisfying the Moufang identity 1.2 were studied in (5). Quasi-fields satisfying the left Bol identity 1.3 were studied by Burn (3) and the author (6). Such quasi-fields are called Bol quasi-fields.Our investigation will parallel the investigations in (5; 6). In § 2 we derive necessary and sufficient conditions for a right Bol quasi-field to be an alternative division ring and also criteria for it to be a near-field. With this information we derive in §§ 3 and 4 new characterizations of Moufang planes similar to those in (5; 6).Loops satisfying (1.1) have been studied by Robinson (10). He calls such loops Bol loops. 
Kallaher, Michael J. Right Bol Quasi-Fields. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1409-1420. doi: 10.4153/CJM-1969-155-8
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