Abstract We compute the generator rank of a subhomogeneous $C^*\!$ -algebra in terms covering dimension pieces its primitive ideal space corresponding to irreducible representations fixed dimension. deduce that every $\mathcal {Z}$ -stable approximately algebra has one, which means generic element such an is generator. This leads strong solution problem for classifiable, simple, nuclear -algebr...

An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples. Introduction. The question of the irreducibility of an ordinary linear differential operator is of interest in the Picard-Vessiot theory (see Kolchin [1, §22]). Indeed, the operator is irreducible if and o...

In this study, we first introduce the fuzzy sets, soft sets, fuzzy soft sets and their related properties. We then present the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that is one of classical Multiple Attribute Decision Making (MADM) methods. We also present the Grey Relation Method. In the main part of this study, we extend the TOPSIS method on the fuzzy soft se...

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduc...

‎‎here we construct and count all ordinary irreducible characters of sylow $p$-subgroups of the steinberg triality groups ${}^3d_4(p^{3m})$.

Let K be a complete field with a discrete valuation v, ring of integers OK , and maximal ideal (πK). Let k := OK/(πK) be the residue field, assumed to be separably closed of characteristic p ≥ 0. LetX/K be a smooth proper geometrically irreducible curve of genus g ≥ 1. Let X /OK denote a regular model of X/K. Let Xk = ∑v i=1 riCi be its special fiber, where Ci/k is an irreducible component of X...

Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish new relation between the Goldie rank of primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and dimension corresponding irreducible representation $V$ an appropriate finite W-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is index suitable equivariant Azumaya algebra on homogeneous s...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

Let A be a polynomial ring in n+ 1 variables over an arbitrary infinite field k. It is proved that for all sufficiently large n and d there is a homogeneous prime ideal p ⊂ A satisfying the following conditions. The ideal p corresponds to a component, defined over k and irreducible over s k, of a projective algebraic variety given by a system of homogeneous polynomial equations with polynomials...