Parastrophic invariance of Smarandache quasigroups
| dc.creator | Jaiyeola, Temitope Gbolahan | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:14:51Z | |
| dc.date.available | 2026-07-07T08:14:51Z | |
| dc.description | Every quasigroup $(L,\cdot)$ belongs to a set of 6 quasigroups, called parastrophes denoted by $(L,π_i)$, $i\in \{1,2,3,4,5,6\}$. It is shown that $(L,π_i)$ is a Smarandache quasigroup with associative subquasigroup $(S,π_i) \forall i\in \{1,2,3,4,5,6\}$ if and only if for any of some four $j\in \{1,2,3,4,5,6\}$, $(S,π_j)$ is an isotope of $(S,π_i)$ or $(S,π_k)$ for one $k\in \{1,2,3,4,5,6\}$ such that $i\ne j\ne k$. Hence, $(L,π_i)$ is a Smarandache quasigroup with associative subquasigroup $(S,π_i) \forall i\in \{1,2,3,4,5,6\}$ if and only if any of the six Khalil conditions is true for any of some four of $(S,π_i)$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0707.1420 | |
| dc.identifier | http://arxiv.org/abs/0707.1420 | |
| dc.identifier | Scientia Magna Journal, Vol. 2, No. 3 (2006), pp. 48-53 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133277 | |
| dc.subject | General Mathematics | |
| dc.subject | 20NO5; 08A05 | |
| dc.title | Parastrophic invariance of Smarandache quasigroups | |
| dc.type | text |