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...

Infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra. The quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal, which defines a toric subvariety in a product of projective lines. Connections to graphic arrangements and to Beilinson’s spectral sequence ...

Let A be a unital AH-algebra and let α ∈ Aut(A) be an automorphism. A necessary condition for A ⋊α Z being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism κ with κ∗1 = −idK1(A) such that α ◦ κ and κ ◦ α are asymptotically unitarily equivalent, then A⋊α Z can be embedded into a unital simple AF-algebra. Consequently,...

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].