/pdf/on-the-foundations-of-quasigroups-3h8ofl3rlg.pdf

On the foundations of quasigroups

Polygroups derived from cogroups

New hyperfields, that is fields in which addition is multivalued, are introduced and studied In a separate paper these hyperfields are shown to provide a base for the tropical geometry The main hyperfields considered here are classical number sets, such as the set of complex numbers, the set of real numbers, and the set of real non-negative numbers, with the usual multiplications, but new, multivalued additions The new hyperfields are related with the classical fields and each other by dequantisations For example, the new complex tropical field is a dequantization of the field of complex numbers

Hyperfields for Tropical Geometry I. Hyperfields and dequantization

Foundations of quasigroups.

/pdf/homomorphisms-and-subalgebras-of-multialgebras-3gvaz3bpow.pdf

Homomorphisms and subalgebras of multialgebras.

Theory of Multigroups

Theory of Quasi-Groups

Remarks on Multigroups

On Generalized Rings

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Theory of Multigroups

Theory of Quasi-Groups

Remarks on Multigroups

On Generalized Rings