Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
New identities in universal Osborn loops
Authors: T. G. Jaiyeola, J. O. Adeniran
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Abstract
A question associated with the 2005 open problem of Michael Kinyon (Is every Osborn loop universal?), is answered. Two nice identities that characterize universal (left and right universal) Osborn loops are established. Numerous new identities are established for universal (left and right universal) Osborn loops like CC-loops, VD-loops and universal weak inverse property loops. Particularly, Moufang loops are discovered to obey the new identity [y(x-1u). u-1](xu)=[y(xu).u-1](x-1u) surprisingly. For the first time, new loop properties that are weaker forms of well known loop properties like inverse property, power associativity and diassociativity are introduced and studied in universal (left and right universal) Osborn loops. Some of them are found to be necessary and sufficient conditions for a universal Osborn to be 3 power associative. For instance, four of them are found to be new necessary and sufficient conditions for a CC-loop to be power associative. A conjugacy closed loop is shown to be diassociative if and only if it is power associative and has a weak form of diassociativity.Fulltext
– 0.31 Mb
Contents
- Kernel normal system of inverse AG**-groupoids
- Products of the symmetric or alternating groups with L3(3)
- Rigid and super rigid quasigroups
- N-quasigroups
- Uniform topology and spectral topology on hyper MV-algebras
- New identities in universal Osborn loops
- LGS-quasigroups
- Generating huge quasigroups from small non-linear bijections via extended Feistel function
