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Abstrakty
In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the related relation defined on this structure is transitive and prove that every pseudo upper set is a pseudo filter. Also, the pseudo filter generated by a set is define and show that the set of all pseudo filters is distributive complete lattice but it is not complemented. the notion of prime and irreducible subset and prove that every irreducible subset is prime.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
21--39
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Department of Mathematici Shahid Beheshti University of Tehran, Tehran, Iran
autor
- Department of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Kerman
autor
- Department of Mathematics Payame Noor University, Tehran, Iran
autor
- Department of Mathematics Payame Noor University, Tehran, Iran
autor
- Department of Mathematics Tehran University, Tehran, Iran
Bibliografia
- [1] Borzooei R.A., Borumand Saeid A., Rezaei A., Radfar A., Ameri R., On pseudo BE-algebras, Discussiones Mathematica, General Algebra and Ap-plicatins, 33(2013), 95-108.
- [2] Georgescu G., Iorgulescu A., Pseudo-MV algebras, Multi. Val. Logic, 6(2001), 95-135.
- [3] Georgescu G., Iorgulescu A., Pseudo-BL algebras: a noncommutative extension of BL algebras, in Abstracts of the Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92.
- [4] Georgescu G., Iorgulescu A., Pseudo-BCK algebras: an extension of BCK-algebras, Combinatorics, computability and logic, 97-114, Springer Ser. Discrete Math. Theor. Comput. Sci., Springer, London, 2001.
- [5] Kim H.S., Kim Y.H., On BE-algebras, Sci, Math, Jpn, 66(1)(2007), 113-117.
- [6] Rachunek J., A non commutative generalization of MV-algebras, Czehoslovak Math. J., 52(127)(2)(2002), 255-273.
- [7] Walendziak A., On axiom systems of pseudo-BCK algebras, Bull. Malays. Math. Sci. Soc., 34(2)(2011), 287-293.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-74d2ab62-5a43-4268-9bd6-888805807daa