The relative densities of rational primes q, such that a given rational prime p is a square of either a principal or a non-principal ideal in the quadratic number field Q( √ pq), essentially depend on the residue classes of both p and q modulo 4. The computation of these densities is complete when at least one residue of p or q is not equal to 1 modulo 4. When both residues are equal to 1 modul...

We define a Riesz type interpolation property for the Cuntz semigroup of a C∗-algebra and prove it is satisfied by the Cuntz semigroup of every C∗-algebra with the ideal property. Related to this, we obtain two characterizations of the ideal property in terms of the Cuntz semigroup of the C∗-algebra. Some additional characterizations are proved in the special case of the stable, purely infinite...

We consider the ideal structure of a reduced crossed product unital C∗-algebra equipped with an action discrete group. More specifically we find sufficient and necessary conditions for group to have intersection property, meaning that non-zero ideals in restrict underlying C∗-algebra. show property on is equivalent equivariant injective envelope. also centre envelope always contains C∗-algebrai...

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic cross-correlations. These sequences are decimations of the 2-adic expansions of rational numbers p/q such that 2 is a primitive root modulo q.

To achieve high resource utilization for multi-issue Digital Signal Processors (DSPs), production compilers commonly include variants of the iterative modulo scheduling algorithm. However, excessive cyclic data dependences, which exist in communication and media processing loops, often prevent the modulo scheduler from achieving ideal loop initiation intervals. As a result, replicated functiona...

We prove the existence of a subset, with positive natural density, squarefree integers n>0 such that 4–rank ideal class group ℚ(-n,n) is ω 3 (n)-1, where (n) number prime divisors n are modulo 4. Recall for groups associated to ℚ(n) or ℚ(-n) an analogous subset does not exist.

An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic crosscorrelations. These sequences are decimations of the 2adic expansions of rational numbers p=q such that 2 is a primitive root modulo q.

We show that a ring $R$ has stable range one if and only every left unit lifts modulo principal ideal. also quasi-morphic it is uniquely generated. Thus we answer in the affirmative two questions raised by W. K. Nicholson.

Let k be an algebraic number eld with maximal order o k and let m 0 be an ideal of o k. We develop an algorithm for the computation of the multiplicative group (o k =m 0) of the residue class ring o k =m 0. It is applied to the computation of the ray class group Cl m k modulo m = m 0 m 1 , where m 1 denotes a formal product of real innnite places, and also to the computation of the conductor of...