Binary relations between binary operations
| dc.contributor.advisor | Козеренко, Сергій | |
| dc.contributor.author | Bilyi, Illia | |
| dc.date.accessioned | 2022-01-19T07:33:23Z | |
| dc.date.available | 2022-01-19T07:33:23Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | Let Bin(X) be a collection of all groupoids on some non-empty set X. De ne the operation : Bin2(X) ! Bin(X) so that x( )y = (x y) (y x) for all x; y 2 X and (X; ); (X; ) 2 Bin(X). Let lz denote left-zero operation (8x; y 2 X : x lz y = x) on X. Then, (X; lz) is an identity of (Bin(X); ). Similarly, de ne right-zero rz 2 Bin(X) (8x; y 2 X : x rz y = y). We consider the center of (Bin(X); ) and represent its elements as graphs. Furthermore, we investigate distributivity from the left in Bin(X) and its interaction with -product. We show that the only operation that is left- distributive over all possible 2 Bin(X) is rz 2 Bin(X) and that any 2 Bin(X) is left-distributive over lz; rz 2 Bin(X). | uk_UA |
| dc.identifier.uri | https://ekmair.ukma.edu.ua/handle/123456789/22332 | |
| dc.language.iso | en | uk_UA |
| dc.status | first published | uk_UA |
| dc.subject | Groupoid | uk_UA |
| dc.subject | Bin(X) | uk_UA |
| dc.subject | left-distributivity | uk_UA |
| dc.subject | graph of groupoid | uk_UA |
| dc.subject | bachelor thesis | uk_UA |
| dc.title | Binary relations between binary operations | uk_UA |
| dc.type | Other | uk_UA |