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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, we generalize various results of nite AG-groupoids by removing the condition of existence of left identity.
📌 3 Key Takeaways
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Objective & Hypothesis:An Abel-Grassmann's groupoid (brie y AG-groupoid) is a groupoid S satisfying the left invertive law: (xy)z = (zy)x for all x, y, z \in S.
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Key Findings & Data:In the present paper, wediscuss the left and right cancellative property of elements of the nite AG-groupoid S.
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Conclusion & Impact:Moreover, we generalize various results of nite AG-groupoids by removing the condition of existence of left identity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:AG-groupoid · AG-subgroupoid · Cancellative elements
Abstract
An Abel-Grassmann's groupoid (brie y AG-groupoid) is a groupoid S satisfying the left invertive law: (xy)z = (zy)x for all x, y, z \in S. In the present paper, wediscuss the left and right cancellative property of elements of the nite AG-groupoid S. For an AG-groupoid with left identity it is known that every left cancellative ele-ment is right cancellative. We prove a problem (for nite AG-groupoids) that every left cancellative element of an AG-groupoid (without left identity) is right cancella-tive. Moreover, we generalize various results of nite AG-groupoids by removing the condition of existence of left identity.
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Cite This Article
KHAN, M., KHAN, A., KHAN, M. U. (2020). Cancellative Elements in Finite AG-groupoids. Journal of New Theory, Sayı: 30, 53–56. https://ajindex.com/articles/681510