The Borel cardinality of the quotient of the power set of the natural numbers by the ideal Z0 of asymptotically zero-density sets is shown to be the same as that of the equivalence relation induced by the classical Banach space c0. We also show that a large collection of ideals introduced by Louveau and Veličkovič, with pairwise incomparable Borel cardinality, are all Borel reducible to c0. Thi...

Cuntz-Krieger algebras with exactly one non-trivial closed ideal are classiied up to stable isomorphism by the Cuntz invariant. The proof relies on RRrdam's classiication of simple Cuntz-Krieger algebras up to stable isomorphism and the author's classiication of two-component reducible topological Markov chains up to ow equivalence.

We consider the Hilbert scheme Hilb(Cd) of (d + 1) points in affine d-space C (d ≥ 3), which includes the square of any maximal ideal. We describe equations for the most symmetric affine open subscheme of Hilb(Cd), in terms of Schur modules. In addition we prove that Hilb(Cd) is reducible for n > d ≥ 12.

Self-assembled monolayers (SAMs) of a mu 3-eta 2:eta 2:eta 2-C60 triosmium cluster complex Os3(CO)8(CN(CH2)3Si(OEt)3)(mu 3-eta 2:eta 2:eta 2-C60) (2) on ITO or Au surface exhibit ideal, well-defined electrochemical responses and remarkable electrochemical stability being reducible up to tetranionic species in their cyclic voltammograms.

If the arity of a maximal irreducible retractof an n-quasigroup M belongs to {3, . . . , n − 3}, then M is reducible.

We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme S, given the homogeneous ideal of S. The algorithm has been implemented in Macaulay2.

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...

We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring Z[[x]] of formal power series with integer coefficients. For n,m ≥ 1 and p prime, we show that p+pβx+αx is reducible in Z[[x]] if and only if it is reducible in Zp[x], the ring of polynomials over the p-adic integers.