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- W3152729452 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." @default.
- W3152729452 created "2021-04-26" @default.
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- W3152729452 date "2021-02-22" @default.
- W3152729452 modified "2023-10-02" @default.
- W3152729452 title "A Study of Completely Inverse Paramedial AG-Groupoids" @default.
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- W3152729452 doi "https://doi.org/10.52280/pujm.2021.530202" @default.
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