The Structure of Digroups | Zendy

Catherine Crompton | Zendy; Linda Scalici | Zendy

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The Structure of Digroups

Author(s) -

Catherine Crompton,

Linda Scalici

Publication year - 2006

Publication title -

american journal of undergraduate research

Language(s) - English

Resource type - Journals

eISSN - 2375-8732

pISSN - 1536-4585

DOI - 10.33697/ajur.2006.016

Subject(s) - axiom , binary operation , associative property , set (abstract data type) , algebra over a field , mathematics , set theory , pure mathematics , discrete mathematics , computer science , geometry , programming language

A digroup is an algebra defined on a set having two associative binary operations, ⊢ and ⊣. Digroups play an important role in an open problem in the theory of Leibniz algebras. We present a brief overview of digroups and a set of more general axioms for a digroup than used previously. We then consider several properties of a digroup having distinct elements a and b such that a ⊢ b = b ⊢ a, but a ⊢ b ≠ a ⊣ b.

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