Chein, Orin; Goodaire, Edgar G. Bol loops with a large left nucleus. (English) Zbl 1192.20051 Commentat. Math. Univ. Carol. 49, No. 2, 171-196 (2008). Starting with an Abelian group \(N\) and a pair of suitable bijections, a power associative loop \(L\) is presented such that the support of \(N\) is a subloop of index 2 contained in the left nucleus of \(L\); a criterion is given when \(L\) is a group. The construction plays the key role in what follows. Possession of a unique nonidentity commutator/associator in a loop is discussed in connection with loop rings. Non-associative Bol loops whose rings in characteristic 2 are strongly right alternative (SRAR loops) are characterized, investigated, and interesting examples are given. Reviewer: Alena Vanžurová (Olomouc) Cited in 1 Document MSC: 20N05 Loops, quasigroups 17D15 Right alternative rings Keywords:nonassociative Bol loops; left nuclei; centre; commutators; associators; strongly right alternative rings; loop rings; power associative loops PDFBibTeX XMLCite \textit{O. Chein} and \textit{E. G. Goodaire}, Commentat. Math. Univ. Carol. 49, No. 2, 171--196 (2008; Zbl 1192.20051) Full Text: EuDML EMIS