Distributive pseudo BE-algebras

• Autorzy: Borzooei R. A. , Saeid A. B. , Rezaei A. , Radfar A. , Ameri R.

Identyfikatory

DOI

10.1515/fascmath-2015-0002

• Języki publikacji: EN

Abstrakty

EN

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

EN

(distributive)pseudo BE-algebra; (normal)pseudo filter; pseudo upper set

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2015
• Tom: Nr 54
• Strony: 21--39
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Borzooei R. A.

• Department of Mathematici Shahid Beheshti University of Tehran, Tehran, Iran

autor

Saeid A. B.

• Department of Pure Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Kerman

autor

Rezaei A.

• Department of Mathematics Payame Noor University, Tehran, Iran

autor

Radfar A.

• Department of Mathematics Payame Noor University, Tehran, Iran

autor

Ameri R.

• 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.