Involutory BE-algebras

• Autorzy: Borzooei R. A. , Borumand Saeid A. , Ameri R. , Rezaei A.

Identyfikatory

DOI

10.7862/rf.2014.2

• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.

Słowa kluczowe

EN

bounded BE-algebra; involutory BE-algebra; involution; semi-lattice; lattice; semisimple algebra

PL

BE-algebra

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2014
• Tom: Vol. 37
• Strony: 13--26
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Borzooei R. A.

• Dept. of Math., Shahid Beheshti University of Tehran, Tehran, Iran

autor

Borumand Saeid A.

• Dept. of. Math., Tehran University, Tehran, Iran

autor

Ameri R.

• Dept. of Math., Shahid Bahonar University of Kerman, Kerman, Iran

autor

Rezaei A.

• Dept. of Math., Payame Noor University, p.o. box. 19395-3697, Tehran, Iran

Bibliografia

• [1] S. S. Ahn and Y. H. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68, No. 2(2008), 279-285.
• [2] S. S. Ahn and K. S. So, On generalized upper sets in BE-algebras, Bull. Korean Math. Soc. 46, No. 2(2009), 281-287.
• [3] S. S. Ahn, Y. H. Kim and J. M. Ko, Filters in commutative BE-algebras, Bull. Korean Math. Soc. 27, No. 2(2012), 233-242.
• [4] A. Borumand Saeid, A. Rezaei and R. A. Borzooei, Some types of lters in BE-algebras, Math. Comput. Sci. Vol. 6, No 3 (2013), 341-352.
• [5] R. A. Borzooei, A. Borumand Saeid, R. Ameri and A. Rezaei, States in BE-algebras, Kochi Journal of Mathematics, Kochi Journal of Mathematics, 9 (2014), 27-42.
• [6] A. Diego, Sur algebra de Hilbert, Logique Math. Ser. A, 21(1967), 177-198.
• [7] H. S. Kim and Y. H. Kim, On BE-algebras, Sci, Math, Jpn. 66, No. 1(2007), 113-116.
• [8] Y. Huang, BCI-algebra, Science Press, Beijing 100717, China, (2006).
• [9] R. Halas, Remarks on commutative Hilbert algebras, Mathematica Bohemica, 127, No. 4(2002), 525-529.
• [10] J. Meng, Implication algebras are dual to Implicative BCK-algebras, Soochow Journal of Math. V. 22, No. 4(1996), 567-571.
• [11] B. L. Meng, On filters in BE-algebras, Sci. Math. Jpn. 71(2010), 201-207.
• [12] A. Rezaei and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX (2012), 33-44.
• [13] A. Rezaei and A. Borumand Saeid, Commutative ideals in BE-algebras, Kyungpook Math. J. 52(2012), 483-494.
• [14] A. Rezaei, A. Borumand Saeid and R. A. Borzooei, Relation between Hilbert algebras and BE-algebras, Appl. Math. 8. No 1 (2013), 573-574.
• [15] A.Walendziak, On commutative BE-algebras, Sci.Math. Jpn. 69, No. 2(2008), 585-588.