Abstract
A magma S that meets the identity, xy·z = zy·x, ∀x, y, z ∈ S
is called an AG-groupoid. An AG-groupoid S gratifying the paramedial
law: uv · wx = xv · wu, ∀ u, v, w, x ∈ S is called a paramedial AGgroupoid. Every AG-grouoid with a left identity is paramedial. We extend
the concept of inverse AG-groupoid [4, 7] to paramedial AG-groupoid and
investigate various of its properties. We prove that inverses of elements in
an inverse paramedial AG-groupoid are unique. Further, we initiate and
investigate the notions of congruences, partial order and compatible partial
orders for inverse paramedial AG-groupoid and strengthen this idea further to a completely inverse paramedial AG-groupoid. Furthermore, we
introduce and characterize some congruences on completely inverse paramedial AG-groupoids and introduce and characterize the concept of separative and completely separative ordered, normal sub-groupoid, pseudo
normal congruence pair, and normal congruence pair for the class of completely inverse paramedial AG-groupoids. We also provide a variety of
examples and counterexamples for justification of the produced results.
Muhammad Rashad, Imtiaz Ahmad, Faruk Karaaslan. (2021) A Study of Completely Inverse Paramedial AG-Groupoids, Punjab University Journal of Mathematics, Volume-53, Issue-2.
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