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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References
Borzooei RA, Aaly Kologani M (2020) An overview of hyper logical algebras. J Algebraic Hyperstruct Logical Algebras 1(3):31–50
Borzooei RA, Bakhshi M, Zahiri O (2014) Filter theory on hyper residuated lattices. Quasigroups Relat Syst 22:33–50
Borzooei RA, Ganji Saffar B, Ameri R (2013) On hyper EQ-algebras. Ital J Pure Appl Math 31:77–96
Cheng XY, Xin XL (2015) Filter theory on hyper BE-algebras. Ital J Pure Appl Math 35:509–526
Cheng XY, Xin XL (2019) Strong hyper deductive systems in hyper equality algebras. J Shandong Univ (Nat Sci) 54(8):14–19
Cheng XY, Xin XL, Jun YB (2016) Hyper equality algebras. Quant Logic Soft Comput Adv Intell Syst Comput 510:415–428
Cheng XY, Xin XL, Yong Y (2017) Deductive systems in hyper EQ-algebras. J Math Res Appl 37(2):183–193
Ciungu LC (2014) On pseudo-equality algebras. Arch Math Logic 53:561–570
Ciungu LC (2015) Internal states on equality algebras. Soft Comput 19:939–953
Ganji Saffar B, Borzooei RA (2016) Filter theory on good hyper EQ-algebras. Ann Univ Craiova Math Comput Sci Ser 43(2):243–258
Hashemi MA, Borzooei RA (2020) Tense like equality algebras. Categ General Algebraic Struct Appl 13(1):143–166
Hashemi MA, Borzooei RA (2020) Results on hyper equality algebras. J Math Ext 14(3):169–193
Jenei S (2012) Equality algebras. Stud Logica 100:1201–1209
Jenei S, Kóródi L (2013) Pseudo equality algebras. Arch Math Logic 52:469–481
Marty F (1934) Sur une generalization de la notion de group, The 8th Congress Mathematics. Scandinaves, Stockholm 45–49
Novák V, De Baets B (2009) EQ-algebras. Fuzzy Sets Syst 160:2956–2978
Paad A, Bakhshi M (2020) Hyper equality ideals: basic properties. J Algebraic Hyperstruct Logical Algebras 1(2):45–56
Yang Y, Zhu K, Xin XL (2020) Fuzzy weak hyper deductive systems of hyper equality algebras and their measures. J Intell Fuzzy Syst 38(4):4415–4429
Zebardast F, Borzooei RA, Aaly Kologani M (2017) Results on equality algebras. Inf Sci 381:270–282
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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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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