Polynomial identities of bicommutative algebras,Lie and Jordan elements |
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| Authors: | Askar S Dzhumadil’daev Nurlan A Ismailov |
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| Institution: | 1. Institute of Mathematics, Kazakh-British Technical University, Almaty, Kazakhstandzhuma@hotmail.com;3. Department of Mathematics and Natural Sciences, Suleyman Demirel University, Kaskelen, Kazakhstan |
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| Abstract: | ABSTRACTAn algebra with identities a(bc)?=?b(ac), (ab)c?=?(ac)b is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan. |
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| Keywords: | Bicommutative algebras Jordan elements Lie elements polynomial identities |
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