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On Annihilators in Hoops

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Abstract

We define the notions of annihilators in hoops and study some related attributes of them, and we show that annihilators are ideals of hoop. In addition, we show that all ideals of hoop are a bounded distributive pseudo-complement lattice, and we use this result and demonstrate that the collection of all annihilators of hoop is a Boolean algebra. Also, we use the notion of annihilator and introduce the special kind of ideal of hoop as \(\varsigma \)-ideal and display that all \(\varsigma \)-ideals of hoop are a complete distributive lattice and we consequence that under what condition it is a Boolean algebra.

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Acknowledgements

The authors are very indebted to the editor and anonymous referees for their careful reading and valuable suggestions which helped to improve the readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei & Y. B. Jun

  2. Hatef Higher Education Institute, Zahedan, Iran

    M. Aaly Kologani

  3. School of Mathematics, Northwest University, Xi’an, 710127, China

    X. L. Xin

  4. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Y. B. Jun

Authors
  1. R. A. Borzooei
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  2. M. Aaly Kologani
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  3. X. L. Xin
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  4. Y. B. Jun
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Correspondence to R. A. Borzooei.

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Borzooei, R.A., Kologani, M.A., Xin, X.L. et al. On Annihilators in Hoops. Soft Comput 26, 6969–6980 (2022). https://doi.org/10.1007/s00500-022-07193-7

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