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Filter theory on hyper equality algebras

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Abstract

In this paper, some results related to properties of various versions in equality algebras are given by using the notion of hyper equality algebras. We introduce some types of filters such as implicative, positive implicative and fantastic filters on hyper equality algebras and prove some results determining the relation between these filters. Further, it is shown that every (\(S_\sim \)-reflexive) positive implicative filter of a hyper equality algebra \(\mathcal {H}\) is a weak (strong) filter of \(\mathcal {H}\). Finally, we prove that every \(S_\sim \)-reflexive implicative filter of \(\mathcal {H}\) is a (fantastic filter) positive implicative filter of \(\mathcal {H}\).

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Acknowledgements

The authors would like to thank Editor-in-Chief, Associate Editor and the anonymous referees for their valuable comments, which greatly improved the quality and clarity 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 & M. Aaly Kologani

  2. Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

    M. A. Hashemi

Authors
  1. R. A. Borzooei
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  2. M. Aaly Kologani
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  3. M. A. Hashemi
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Correspondence to R. A. Borzooei.

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Borzooei, R.A., Kologani, M.A. & Hashemi, M.A. Filter theory on hyper equality algebras. Soft Comput 25, 7257–7269 (2021). https://doi.org/10.1007/s00500-021-05832-z

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  • DOI: https://doi.org/10.1007/s00500-021-05832-z

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