Abstract
A groupoid with the left invertive law is an LA-semigroup or
an Abel-Grassmann’s groupoid (AG-groupoid). This in general is a nonassociative structure that lies between a groupoid and a commutative semigroup. In this note, the significance of the left Abelian distributivie (LAD)
LA-semigroup is considered and investigated as a subclass. Various relations with some other known subclasses are established and explored.
A hard level problem suggested for LAD-LA-semigroup to be self-dual
[29] is solved. Moreover, the notion of ideals is introduced and characterized for the subclass. Several examples and counterexamples generated
with the modern tools of Mace-4 and GAP are produced to improve the
authenticity of investigated results.
Imtiaz Ahmad, Saif-ur-Rahman, Muhammad Iqbal, Amanullah. (2020) A Note on Left Abelian Distributive LA-semigroups, Punjab University Journal of Mathematics, Volume 52 , Issue No.1.
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