| Title:
|
The commingling of commutativity and associativity in Bol loops (English) |
| Author:
|
Phillips, J. D. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
555-565 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Bol |
| Keyword:
|
Moufang |
| Keyword:
|
loop |
| Keyword:
|
commutant |
| Keyword:
|
associator |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 06674897 |
| idMR:
|
MR3583307 |
| DOI:
|
10.14712/1213-7243.2015.185 |
| . |
| Date available:
|
2017-01-09T22:20:25Z |
| Last updated:
|
2019-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145945 |
| . |
| Reference:
|
[1] Bruck R.H.: A Survey of Binary Systems.Springer, Berlin-Göttingen-Heidelberg, 1971. Zbl 0141.01401, MR 0093552 |
| Reference:
|
[2] Florja I.A.: Loops with one-sided invertibility.Bul. Akad. Štiince RSS Moldoven (1965), no. 7, 68–79. MR 0197613 |
| Reference:
|
[3] Kinyon M.K., Phillips J.D.: Commutants of Bol loops of odd order.Proc. Amer. Math. Soc. 132 (2004), no. 3, 617–619. Zbl 1044.20041, MR 2019935, 10.1090/S0002-9939-03-07211-3 |
| Reference:
|
[4] McCune W.W.: Prover9 $3.3$ Reference Manual and Guide.Argonne National Laboratory Technical Memorandum ANL/MCS-TM-263, 2003; http://www.mcs.anl.gov/AR/Prover9/. |
| Reference:
|
[5] McCune W.W.: Mace $4.0$ Reference Manual and Guide.Argonne National Laboratory Technical Memorandum ANL/MCS-TM-264, 2003; http://www.mcs.anl.gov/AR/mace4/. |
| Reference:
|
[6] McCune W.W., Padmanabhan R.: Automated Deduction in Equational Logic and Cubic Curves.Springer, Berlin, 1996. Zbl 0921.03011, MR 1439047 |
| Reference:
|
[7] Phillips J.D.: The Moufang laws, global and local.J. Algebra Appl. 8 (2009), no. 4, 477–492. Zbl 1190.20052, MR 2555515, 10.1142/S021949880900345X |
| . |
