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On BE-ringoids

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Abstract

The concept of BE-ringoid is introduced, and some properties of it are investigated. We discuss on a distributive BE-ringoid. Further, transitive BE-ringoid is defined and the relationship between distributive BE-ringoids and transitive BE-ringoids is considered, and we prove that every distributive BE-ringoid is a transitive BE-ringoid, but the converse may not be true, and an example is given to illustrate it.

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References

  • Ahn SS, Kim YH (2011) On BE-semigroups, Int. J. Math. Math. Sci. Article ID 676020, 8 pages

  • Borzooei RA, Borumand Saeid A, Ameri R, Rezaei A (2014) Involutory BE-algebras. J Math Appl 37:13–26

    MATH  Google Scholar 

  • Huang Y (2006) BCI-algebras. Science Press, Beijing

    MATH  Google Scholar 

  • Iorgulescu A (2008) Algebras of logic as BCK-algebras. Editura ASE, Bucharest

    MATH  Google Scholar 

  • Iorgulescu A (2008) On BCK algebras: Part II: New algebras. The ordinal sum (product) of two bounded BCK algebras. Soft Comput 12:835–856

    Article  MATH  Google Scholar 

  • Kim HS, Kim YH (2007) On BE-algebras. Sci Math Jpn 66:113–116

    MATH  Google Scholar 

  • Meng J, Jun YB (1994) BCK-algebras. Kyungmoon Sa, Seoul

    MATH  Google Scholar 

  • Neggers J, Kim HS, Rezaei A (2022) On ringoids, J Algebr Hyperstructures Log Algebr (to appear)

  • Rezaei A, Borumand Saeid A, Borzooei RA (2013) Relation between Hilbert algebras and BE-algebras. Appl Appl Math 8(2):573–584

    MATH  Google Scholar 

  • Walendziak A (2008) On commutative BE-algebra. Sci Math Jpn 69(2):281–284

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

    A. Rezaei & S. Borhani Nejad Rayeni

  2. Department of Mathematics, Hanyang University, Seoul, 04763, Korea

    Hee Sik Kim

Authors
  1. A. Rezaei
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  2. S. Borhani Nejad Rayeni
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  3. Hee Sik Kim
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Correspondence to A. Rezaei.

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Rezaei, A., Borhani Nejad Rayeni, S. & Kim, H.S. On BE-ringoids. Soft Comput 27, 1379–1388 (2023). https://doi.org/10.1007/s00500-022-07637-0

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  • DOI: https://doi.org/10.1007/s00500-022-07637-0

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