Related papers: Algebraic approximation preserving dimension
We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient…
We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.
The H\"older continuity of the truncated moment map of a shade function in Euclidean space is established in the vicinity of a principal semi-algebraic set. The proof combines volume bounds of semi-algebraic sets and convex optimization…
Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
We present a criterion of local Normal Embedding of a semialgebraic (or definable in an o-minimal structure) contained in $R^n$ in terms orders of contact of arcs. Namely, we prove that a semialgebraic set is normally embedded at a point x…
We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…
We show that a projective triangulation of a subcomplex of a polyhedral complex can be extended to the whole complex. As a result, we show that the weak semistable reduction result of Abramovich - Karu alg-geom/9707012 can be refined, so…
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
A complete contraction on a C*-algebra A, which preserves all closed two sided ideals J, can be approximated pointwise by elementary complete contractions if and only if the induced map on the tensor product of B with A/J is contractive for…
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
In this work we prove a criterion for an algebraic continued fraction to have a proper palindromic symmetry in dimension $4$. As a multidimensional generalization of continued fractions, we consider Klein polyhedra.
In the present paper we prove that every local and $2$-local derivation on conservative algebras of $2$-dimensional algebras are derivations. Also, we prove that every local and $2$-local automorphism on conservative algebras of…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of…
Real algebraic geometry is the study of semi-algebraic sets, subsets of $\R^k$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry,…
The matrix units of a digraph algebra, A, induce a relation, known as the diagonal order, on the projections in a masa in the algebra. Normalizing partial isometries in A act on these projections by conjugation; they are said to be order…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
In this article we introduce the notion of badly approximable matrices of higher order using higher sucessive minima in $\mathbb R^d$. We prove that for order less than $d$, they have Lebesgue measure zero and the gaps between them still…
Let A subset R^n be a set-germ at 0 in R^n such that 0 is in the closure of A. Let D(A) denote the set of all directions of A at 0 in R^n. Let A, B subsets R^n be subanalytic set-germs at 0 in R^n such that 0 belongs to their closure. We…