Document Details Document Type : Article In Journal  Document Title : On annihilators of BCK-algebras On annihilators of BCK-algebras   Document Language : Arabic  Abstract : Let X be a commutative BCK-algebra and A an ideal of X. To any subset B of X we associate the set (A : B) = {x is an element of x Lambda B subset of or equal to A}, where x Lambda B = {x Lambda y: y is an element of B}. We show that (A : B) is an ideal of X and define it as the generalized annihilator of B (relative to A). If A = {0}, then (A : B) coincides with the usual annihilator of B (see for instance [4]). These and some other properties of generalized annihilators are contained in Section 3 of this paper. Section 4 contains some applications of generalized annihilators in quotient BCK-algebras and in the theory of prime ideals of BCK-algebras. Using the technique of generalized annihilators, we show that the quotient BCK-algebra of an involutory BCK-algebra is again an involutory BCK-algebra. We also obtain a characterization of prime ideals: A categorical ideal A is prime if and only if (A : B) = A (see Proposition 4.9). Section 2 contains some preliminary material for the development of our results.  Journal Name : CZECHOSLOVAK MATHEMATICAL JOURNAL  Volume : 45  Issue Number : 4  Publishing Year : 1995 AH   Added Date : Saturday, June 14, 2008  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email حمزة علي أبو جبل Abujabal HAS Researcher     . Obaid MA Researcher     . Aslam M Researcher     . Thaheem AB Researcher     Back To Researches Page