2014/03/20 by Muhammad Rashad, Imtiaz Ahmad, Rashad, Muhammad +3
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Fuzzy and Soft Set Theory #math.GR #msc:20N02
paper · pdf · doi:10.48550/arxiv.1403.5218
10 pages
arxiv created 2014/03/20 · arxiv updated 2014/03/21
A groupoid that satisfies the left invertive law: ab⋅ c=cb⋅ a is called an AG-groupoid. We extend the concept of left abelian distributive groupoid (LAD) and right abelian distributive groupoid (RAD) to introduce new subclasses of AG-groupoid, left abelian distributive AG-groupoid and right abelian distributive AG-groupoid. We give their enumeration up to order 6 and find some basic relations of these new classes with other known subclasses of AG-groupoids and other relevant algebraic structures. We establish a method to test an arbitrary AG-groupoid for these classes.