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Left regular \({\mathcal{AG}}\)-groupoids in terms of fuzzy interior ideals

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Abstract

The left and right regular classes of a semigroup theory plays essential role in studying the structural properties of the associative algebraic structure. In this paper, we show that these two classes coincides in an \({\mathcal{AG}}\)-groupoid with left identity which is a non-associative algebraic structure. As an application of our results we get characterizations of a left regular \({\mathcal{AG}}\)-groupoid in terms of fuzzy interior ideals and study some important properties in different aspects. Further we introduce a very basic theory for an \({\mathcal{AG}}\)-groupoid in terms of classical and fuzzy (left, right, two-sided, interior) ideals and show that how similar is the theory of an \({\mathcal{AG}}\)-groupoid with the theory of fuzzy \({\mathcal{AG}}\)-groupoid.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

    Faisal

  2. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Naveed Yaqoob

  3. Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

    A. Ghareeb

Authors
  1. Faisal
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  2. Naveed Yaqoob
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  3. A. Ghareeb
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Correspondence to Naveed Yaqoob.

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Faisal, Yaqoob, N. & Ghareeb, A. Left regular \({\mathcal{AG}}\)-groupoids in terms of fuzzy interior ideals. Afr. Mat. 24, 577–587 (2013). https://doi.org/10.1007/s13370-012-0081-y

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  • DOI: https://doi.org/10.1007/s13370-012-0081-y

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