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AN ISOMORPHISM THEOREM FOR ALEXANDER BIQUANDLES

DAISY LAM

Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA, 92521, USA

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and

SAM NELSON

Department of Mathematics, University of California, Riverside, 900 University Avenue, Riverside, CA, 92521, USA

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https://doi.org/10.1142/S0129167X09005194Cited by:4 (Source: Crossref)

Abstract

We show that two Alexander biquandles M and M′ are isomorphic if and only if there is an isomorphism of ℤ[s^±1, t^±1]-modules h : (1 - st)M → (1 - st)M′ and a bijection g : O_s(A) → O_s(A′) between the s-orbits of sets of coset representatives of M/(1 - st)M and M′/(1 - st)M′ respectively satisfying certain compatibility conditions.

Keywords:

AMSC: 57M27, 57M25, 17D99

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