On normal niters and congruence relations in BE-algebras

• Autorzy: Walendziak A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we introduce the notion of a normal filter in BE-algebras (in transitive BE-algebras filters conicide with normal filters). We discuss some relationships between congruence relations and normal filters of a BE-algebra A (if A is commutative, then we show that there is a bijection between congruence relations and niters in A). Moreover, we give the construction of quotient algebra A/F of A via a normal filter F of A.

Słowa kluczowe

EN

BE-algebra; normal filter; congruence relation; transitive BE-algebra; commutative BE-algebra

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: Vol. 52, [Z] 2
• Strony: 199--205
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Walendziak A.

• Institute of Mathematics and Physics, Siedlce University 3 Maja 54, 08 110, Siedlce, Poland

Bibliografia

• [1] S.S. Ahn and K.S. So, On ideals and upper sets in BE-algebras, Scientiae Mathematicae Japonicae 68 (2008), 279-285.
• [2] K.H. Kim, A note on BE-algebras, Scientiae Mathematicae Japonicae 72 (2010), 127-132.
• [3] H.S. Kim and Y.H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae 66 (2007), 113-116.
• [4] H.S. Kim and K.J. Lee, Extended upper sets in BE-algebras, Bull. Malays. Math. Sci. Soc. 34 (2011), 511-520.
• [5] B.L. Meng, On filters in BE-algebras, Scientiae Mathematicae Japonicae 71 (2010), 201-207.
• [6] A. Walendziak, On commutative BE-algebras, Scientiae Mathematicae Japonicae 69 (2009), 281-284.
• [7] Y.H. Yon, S.M. Lee, and K.H. Kim, On congruences and BE-relations in BE-algebras, International Mathematical Forum 5 (2010), 2263-2270.