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2013 | 33 | 1 | 95-108
Tytuł artykułu

On pseudo BE-algebras

Treść / Zawartość
Warianty tytułu
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EN
Abstrakty
EN
In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.
Twórcy
  • Department of Mathematics Shahid Beheshti University of Tehran, Tehran, Iran
  • Department of Mathematics Shahid Bahonar University of Kerman, Kerman, Iran
autor
  • Department of Mathematics, Payame Noor University P.O. Box. 19395-3697, Tehran, Iran
autor
  • Department of Mathematics, Payame Noor University P.O. Box. 19395-3697, Tehran, Iran
autor
  • Department of Mathematics, Tehran University Tehran, Iran
Bibliografia
  • [1] S.S. Ahn and Y.H. So, On ideals and upper sets in BE-algebras, Sci. Math. Jpn. 68 (2) (2008) 279-285.
  • [2] S.S. Ahn and K.S. So, On generalized upper sets in BE-algebras, Bull. Korean Math. Soc. 46 (2) (2009) 281-287. doi: 10.4134/BKMS.2009.46.2.281
  • [3] S.S. Ahn, Y.H. Kim and J.M. Ko, Filters in commutative BE-algebras, Bull. Korean Math. Soc. 27 (2) (2012) 233-242. doi: 10.4134/CKMS.2012.27.2.233
  • [4] A. Borumand Saeid, A. Rezaei and R.A. Borzoei, Some types of filters in BE-algebras, (submitted).
  • [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras, Information Technology (Bucharest, 1999), 961-968, Inforec, Bucharest.
  • [6] G. Georgescu and A. Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras, in Abstracts of the Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92.
  • [7] G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK-algebras, Combinatorics, computability and logic, 97-114, Springer Ser. Discrete Math. Theor. Comput. Sci., Springer, London, 2001.
  • [8] Y. Imai and K. Iseki, On axiom systems of propositional Calculi, XIV proc. Jpn. Academy 42 (1966) 19-22.
  • [9] Y.B. Jun, H.S. Kim and J. Neggers, On pseudo-BCI ideals of pesudo-BCI algebras, Math. Bec. 58 (2006) 39-46.
  • [10] H.S. Kim and Y.H. Kim, On BE-algebras, Sci, Math, Jpn. 66 (1) (2007) 113-117.
  • [11] Y.H. Kim and K.S. So, On minimality in pseudo-BCI algebras, Commun. Korean Math. Soc. 27 (1) (2012) 7-13. doi: 10.4134/CKMS.2012.27.1.007
  • [12] B.L. Meng, On filters in BE-algebras, Sci. Math. Jpn. 71 (2010), 201-207.
  • [13] J. Rachunek, A non commutative generalization of MV-algebras, Czehoslovak Math. J. 52 (127) (2002) 255-273.
  • [14] A. Rezaei and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX (2012), 33-44.
  • [15] A. Rezaei and A. Borumand Saeid, Commutative ideals in BE-algebras, Kyungpook Math. J. 52 (2012) 483-494. doi: 10.5666/KMJ.2012.52.4.483
  • [16] A. Walendziak, On commutative BE-algebras, Sci. Math. Jpn. 69 (2) (2008) 585-588.
  • [17] A. Walendziak, On axiom systems of pseudo-BCK algebras, Bull. Malays. Math. Sci. Soc. 34 (2) (2011) 287-293.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1193
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