| Title:
|
Invertibility criterion of composition of two multiary quasigroups (English) |
| Author:
|
Sokhatsky, Fedir M. |
| Author:
|
Fryz, Iryna V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
429-445 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for $T$-quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and $n$-ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73--86]. We establish some relationships between these notions and give illustrative examples. (English) |
| Keyword:
|
quasigroup |
| Keyword:
|
composition of operations |
| Keyword:
|
orthogonal operations |
| Keyword:
|
perpendicular operations |
| Keyword:
|
hypercube |
| Keyword:
|
perpendicular hypercubes |
| Keyword:
|
orthogonality of hypercubes |
| Keyword:
|
slice |
| Keyword:
|
linear quasigroup |
| Keyword:
|
$T$-quasigroup |
| MSC:
|
05B15 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1258.20059 |
| idMR:
|
MR3017841 |
| . |
| Date available:
|
2012-08-31T11:41:32Z |
| Last updated:
|
2014-10-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142935 |
| . |
| Reference:
|
[1] Gluhov M.M.: About $\alpha$-closed classes and $\alpha$-complete systems of functions of $k$-valued logics.Discrete Math. 1 (1989), no. 1, 16–21. MR 1072636 |
| Reference:
|
[2] Sokhatsky F.M.: The deepest repetition-free decompositions of non-singular functions of finite valued logics.Proceedings of The Twenty-Sixth International symposium on Multiple-Valued Logic (Santiago de Compostela, Spain, May 29-31, 1996), pp. 279–282. |
| Reference:
|
[3] Belousov V.D.: Crossed isotopies of quasigroup.Quasigroups and their Systems, Stiintsa, Chishinau, 1990, 14–20 (in Russian). MR 1073918 |
| Reference:
|
[4] Belyavskaya G.: Pairwise orthogonality of $n$-ary operations.Bul. Acad. Stiinte Repub. Mold. Mat. 3 (2005), 5–18. Zbl 1148.20310, MR 2225091 |
| Reference:
|
[5] Yurevych O.: About cross isotopy of poliagroup.Pratsi Instytutu prykladnoi matematyky i mechaniky NAN Ukraina 11 (2005), 34–39 (in Ukrainian). MR 2353778 |
| Reference:
|
[6] Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and $n$-ary operations.Quasigroups Related Systems 13 (2005), no. 1, 73–86. Zbl 1101.20049, MR 2206148 |
| Reference:
|
[7] Sokhatskyj F., Syvakivskyj P.: On linear isotopes of cyclic groups.Quasigroups Related Systems 1 (1994), no. 1, 66–76. MR 1327947 |
| Reference:
|
[8] Mullen G.L., Shcherbacov V.A.: On orthogonality of binary operations and squares.Bul. Acad. Stiinte Repub. Mold. Mat. 2 (2005), 3–42. MR 2190736 |
| . |
