Showing papers in "Czechoslovak Mathematical Journal in 1995"

On annihilators of BCK-algebras

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 49) Section 2 contains some preliminary material for the development of our results

Examples of sectional curvature with prescribed symmetry on 3-manifolds

Abstract: In a previous paper, we determined the possi- ble pointwise symmetry groups of sectional curvature con- sidered as a rational function. We determined the naturally reductive homogeneous spaces with constant symmetry, and gave general descriptions of some examples of them. Here, we exhibit explicit forms of the metric tensors on some of these examples. We also give some inhomogeneous examples utilizing warped products, and begin the study of how the symmetry type can vary on a connected space.