Let F be a number field with ring of integers OF and D a division F -algebra with a maximal cyclic subfield K. We study rings occurring as quotients of a natural OF -order Λ in D by two-sided ideals. We reduce the problem to studying the ideal structure of Λ/qΛ, where q is a prime ideal in OF , s ≥ 1. We study the case where q remains unramified in K, both when s = 1 and s > 1. This work is mot...

Let $R$ be an associative ring with unity. An element $x \in R$ is called $\mathbb{Z}G$-clean if $x=e+r$, where $e$ is an idempotent and $r$ is a $\mathbb{Z}G$-regular element in $R$. A ring $R$ is called $\mathbb{Z}G$-clean if every element of $R$ is $\mathbb{Z}G$-clean. In this paper, we show that in an abelian $\mathbb{Z}G$-regular ring $R$, the $Nil(R)$ is a two-sided ideal of $R$ and $\fra...

Let T denote the full Toeplitz algebra on the Bergman space of the unit ball Bn. For each subset G of L ∞, let CI(G) denote the closed two-sided ideal of T generated by all TfTg − TgTf with f, g ∈ G. It is known that CI(C(Bn)) = K the ideal of compact operators and CI(C(Bn)) = T. Despite these “extremal cases”, T does contain other non-trivial ideals. This paper gives a construction of a class ...

Carotid artery thrombosis and concomitant brain infarction after blunt trauma are rare conditions. We report a 34-year-old woman with multiple traumas due to pedestrian car accident. At the time of initial visiting, she was somnolent and her Glasgow coma scale (GCS) score was 14. Initial vital signs (V/S) and brain computed tomography (CT) scan were normal. One day after admission to the emerge...

Let R be a commutative ring throughout. Usually R will be an integral domain and even a principal ideal domain, but these assumptions will be made explicitly. Since R is commutative, there is no distinction between left, right and 2-sided ideals. In particular, for every ideal I we have a quotient ring R/I. F always denotes a field. Our goal is to prove the classification theorem for finitely-g...

The asymptotic behavior of the dual filters associated with biorthogonal spline wavelet (BSW) systems and general biorthogonal Coifman wavelet (GBCW) systems are studied. As the order of the wavelet systems approaches infinity, the magnitude responses of the dual filters in the BSW systems either diverge or converge to some nonideal frequency responses. However, the synthesis filters in the GBC...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

We attach a Dixmier algebra B to the closure O of any nilpotent orbit of G where G is GL(n, C), O(n, C) or Sp(2n, C). This algebra B is a noncommutative analog of the coordinate ring R of O, in the sense that B has a G-invariant algebra filtration and grB = R. We obtain B by making a noncommutative analog of the Kraft-Procesi construction which modeled O as the algebraic symplectic reduction of...

Problem 1. Let R be a ring and let M be a left R-module. (a) Let I be a right ideal in R and let IM be the abelian subgroup of M generated by the elements rm, r ∈ I, m ∈M . Then R/I ⊗RM ∼= M/IM as an abelian group. (b) If I is a two-sided ideal, then the isomorphism in (a) is that of left R-modules. (c) Let R be commutative, I, J ⊂ R be ideals. Then R/I ⊗R R/J ∼= R/(I + J) as an R-module. (d) L...

A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements with the coordinates of the ambient space. It is well known that every affine-invariant code of length pm, with p prime, can be realized as an ideal of the ...