We prove that if a right distributive ring R, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of R is the right singular ideal of R and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.

Let R be a noncommutative prime ring with its Utumi ring of quotients U , C = Z(U) the extended centroid of R, F a generalized derivation of R and I a nonzero ideal of R. Suppose that there exists 0 = a ∈ R such that a(F ([x, y]) − [x, y]) = 0 for all x, y ∈ I, where n ≥ 2 is a fixed integer. Then one of the following holds: 1. char (R) = 2, R ⊆ M2(C), F (x) = bx for all x ∈ R with a(b − 1) = 0...

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra A(2) of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq, Sq, and Sq on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in term of the annihilator of the Tho...

Let R be an Archimedean partially ordered ring in which the square of every element is positive, and N(R) the set of all nilpotent elements of R. It is shown that N(R) is the unique nil radical of R, and that N(R) is locally nilpotent and even nilpotent with exponent at most 3 when R is 2-torsion-free. R is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator...

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R) = A(R)r {0} and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal...

Let m,n ∈ N. In this paper we study the right permutation action of the symmetric group S2n on the set of all the Brauer n-diagrams. A new basis for the free Z-module Bn spanned by these Brauer n-diagrams is constructed, which yields Specht filtrations for Bn. For any 2m-dimensional vector space V over a field of arbitrary characteristic, we give an explicit and characteristic-free description ...

Weighted cup-length calculations in singular cohomology led Farber and Grant in 2008 to general lower bounds for the topological complexity of lens spaces. We replace singular cohomology by connective complex K-theory, and weighted cup-length arguments by considerations with biequivariant maps on spheres to improve on Farber–Grant’s bounds by arbitrarily large amounts. Our calculations are base...

We prove Schur–Weyl duality between the Brauer algebra Bn(m) and the orthogonal group Om(K) over an arbitrary infinite field K of odd characteristic. If m is even, we show that each connected component of the orthogonal monoid is a normal variety; this implies that the orthogonal Schur algebra associated to the identity component is a generalized Schur algebra. As an application of the main res...

In this note we investigate the existence of frames of exponentials for L(Ω) in the setting of LCA groups. Our main result shows that sub–multitiling properties of Ω ⊂ Ĝ with respect to a uniform lattice Γ of Ĝ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of Γ. We also prove the converse of this result and provide condit...