Let G = GLn(q) be the general linear group of degree n ≥ 2 defined over a finite field Fq of characteristic p. We fix a prime l 6= p and let stand R for a local principal ideal domain having characteristic 0, maximal ideal lR, and containing a primitive p-th root of unity. Then the residue field K = R/lR has characteristic l and a primitive p-th root of unity. By a Steinberg lattice of G over R...

The article presents some results concerning H-bases and theirs applications in multivariate interpolation. We derived the space of reduced polynomials with respect to a particular inner product. We made some connections with least interpolation and presented two application of the connection between spaces of reduced polynomials modulo a H-basis and spaces of ideal interpolation. 2000 Mathemat...

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study some matrix Using tool, characterize [Formula: see text], provided that text] is uniformly locally finite inverse semigroup. As an application, show Brandt semigroup pseudo-amenable if and only amenable finite. give examples to the differences between other classical notions amenability.

For a quartic primitive CM field K, we say that a rational prime p is evil if at least one of the abelian varieties with CM by K reduces modulo a prime ideal p|p to a product of supersingular elliptic curves with the product polarization. We call such primes evil primes for K. In [GL], we showed that for fixed K, such primes are bounded by a quantity related to the discriminant of the field K. ...

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. study relation between this new with various notions Connes like amenability, approximate and pseudo amenability. also investigate some hereditary properties notion. prove that a locally compact group G,M(G) is amenable if only G amenable. Also we show every non-empty set I,MI(C) under forced to have finite i...

The existence of exact upper bounds for increasing sequences of ordinal functions modulo an ideal is discussed. The main theorem (Theorem 18 below) gives a necessary and suucient condition for the existence of an exact upper bound f for a < I-increasing sequence f = hf : < i On A where > jAj + is regular: an eub f with lim inf I cff(a) = exists if and only if for every regular 2 (jAj;) the set ...

The paper has two objectives. On the one hand, we study left Haar null sets—a measure theoretic notion of smallness on Polish, not necessarily locally compact, groups. On the other hand, we introduce and investigate two classes of Polish groups which are closely related to this notion and to amenability. We show that left Haar null sets form a σ-ideal and have the Steinhaus property on Polish g...

We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals, associated primes, leading term ideals, and the minimal number of generators. In contrast, the reduction number of the Ratliff-Rush filtration behaves better...