We give new proofs of two theorems on rings in which every zero subring is finite; and we apply these theorems to obtain a necessary and sufficient condition for an infinite ring with periodic additive group to have an infinite periodic subring. 2000 Mathematics Subject Classification. 16N40, 16N60, 16P99. Let R be a ring and N its set of nilpotent elements; and call R reduced if N = {0}. Follo...

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) ⊆ L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T (A2n+1) = 2n+1 ∑ i=1 (−1)i+1Ai−1T (A)A2n+1−i, for all A ∈ A(X) and some fixed integer n ≥ 1. In this case T ...

In this paper we prove the following result. LetH be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D : A(H) → L(H) satisfying the relation D(An) = D(A)A∗n−1 + AD(An−2)A∗ + An−1D(A) for all A ∈ A(H) and some fixed integer n > 1. In this case there exists a uniqu...

After the introduction of fuzzy sets by Zadeh [20] in 1965, several researchers have been working on the generalization of the fuzzification. In 1986, Atanassov [2] introduced the notion of intuitionistic fuzzy sets. For more details on the intuitionistic fuzzy sets, we refer to [2-4]. Fuzzy sets are intuitionistic fuzzy sets but the converse is not necessarily true [18]. Kim and Jun [7, 8] int...

In this paper we introduce the notion of intuitionistic fuzzy prime, strongly prime, semiprime bi-ideals in ternary semigroup and look for some of their related characteristics. Also here we introduce irreducible and strongly irreducible intuitionistic fuzzy bi-ideals in a ternary semigroup. AMS subject classification: 20N10, 20M12, 04A72.