GENERALIZED DERIVATIONS WITH LEFT ANNIHILATOR CONDITIONS IN PRIME AND SEMIPRIME RINGS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 2
Abstract
Let R be a prime ring with its Utumi ring of quotients U, C = Z(U) be the extended centroid of R, H and G two generalized derivations of R, L a noncentral Lie ideal of R, I a nonzero ideal of R. The left annihilator of S ⊆ R is denoted by lR(S) and defined by lR(S) = {x ∈ R | xS = 0}. Suppose that S = {H(un)un + unG(un)| u ∈ L} and T = {H(xn)xn + xnG(xn)| x ∈I}, where n ≥ 1 is a fixed integer. In the paper, we investigate the cases when the sets lR(S) and lR(T ) are nonzero. Keywords: prime ring, derivation, Lie ideal, generalized derivation, extended centroid, Utumi quotient ring. 2010 Mathematics Subject Classification: 16W25, 16W80, 16N60.
Authors and Affiliations
Basudeb Dhara
Keywords
Related Articles
- EP ID EP304569
- DOI -
- Views 25
- Downloads 0
RELATION BETWEEN (FUZZY) GODEL IDEALS AND ¨ (FUZZY) BOOLEAN IDEALS IN BL-ALGEBRAS
In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) G¨odel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a G¨...
INTRODUCING FULLY UP-SEMIGROUPS
In this paper, we introduce some new classes of algebras related to UPalgebras and semigroups, called a left UP-semigroup, a right UP-semigroup, a fully UP-semigroup, a left-left UP-semigroup, a right-left UP-semigroup,...
SEMIGROUPS DERIVED FROM (Γ, N)-SEMIHYPERGROUPS AND T-FUNCTOR
The main purpose of this paper is to introduce the concept of (Γ, n)- semihypergroups as a generalization of hypergroups, as a generalization of nary hypergroups and obtain an exact covariant functor between the category...
BOOLEAN FILTERS IN PSEUDO-COMPLEMENTED ALMOST DISTRIBUTIVE LATTICES
In this paper we have introduced the concept of Boolean filters in a pseudo-complemented Almost Distributive Lattice (pseudo-complemented ADL) and studied their properties. Finally, a Boolean filter is characterized in t...
COMMUTATIVITY OF PRIME RINGS WITH SYMMETRIC BIDERIVATIONS
The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y]...