Lee, Han Zhou (2025) Magmas And The Twelve Local Moufang Identities. Masters thesis, Perpustakaan Hamzah Sendut.
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Abstract
Quasigroup is a binary system in which the specification of any two of x,y and z in the equation x · y = z determines the third element uniquely. A loop is a quasigroup with a (two-sided) identity element. A magma is a generalization of loops that does not satisfy the quasigroup condition. The (four) moufang identities are identities which are equivalent to each other in the variety of loops, for which a direct and comprehensive proof is provided. Each moufang identity involves three variables. By transforming a variable into a constant in each identity, the four moufang identities can be localized into twelve local identities. However, these local moufang identities are not generally equivalent to each other in the variety of magmas. Hence, this thesis aims to introduce not-too-restrictive conditions to magmas such that relationships can be found between these local identities. The automated reasoning tool prover9 and the finite model builder mace4 are used to obtain some of the important results in this thesis.
| Item Type: | Thesis (Masters) |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA1 Mathematics (General) |
| Divisions: | Pusat Pengajian Sains Matematik (School of Mathematical Sciences) > Thesis |
| Depositing User: | Mr Hasmizar Mansor |
| Date Deposited: | 26 May 2026 01:12 |
| Last Modified: | 26 May 2026 01:12 |
| URI: | http://eprints.usm.my/id/eprint/64277 |
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