Related papers: A new proposal to the extension of complex numbers
We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…
A new dimension function on countable-dimensional algebras (over a field) is described. Its dimension values for finitely generated algebras exactly fill the unit interval $[0,1]$. Since the free algebra on two generators turns out to have…
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…
In this work we explore the construction of abelian extensions of number fields with exactly one complex place using multivariate analytic functions in the spirit of Hilbert's 12th problem. To this end we study the special values of the…
Multiple zeta-star values are variants of multiple zeta values which allow equality in the definition. Similar to the theory of continued fractions, every real number which is greater than $1$ can be realized as an unique infinite multiple…
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties,…
The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…
We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.
The problem of expressing a selfadjoint element that is zero on every bounded trace as a finite sum (or a limit of sums) of commutators is investigated in the setting of C*-algebras of finite nuclear dimension. Upper bounds -- in terms of…
A dichotomy for expansions of the real field is established: Either the set of integers is definable or every nonempty bounded nowhere dense definable subset of the real numbers has Minkowski dimension zero.
V.I. Arnold has recently defined the complexity of a sequence of $n$ zeros and ones with the help of the operator of finite differences. In this paper we describe the results obtained for almost most complicated sequences of elements of a…
Let $\mathcal{A}$ be a separable nuclear C*-algebra, and $\mathcal{B}$ be a nonunital separable simple $\mathcal{Z}$-stable C*-algebra. Continuing the work from Gabe-Lin-Ng, we classify all essential extensions, with large complement, of…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…
We give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive…
The zeta-dimension of a set A of positive integers is the infimum s such that the sum of the reciprocals of the s-th powers of the elements of A is finite. Zeta-dimension serves as a fractal dimension on the positive integers that extends…
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
We examine the representation of numbers as the sum of two squares in $\mathbb{Z}_n$ for a general positive integer $n$. Using this information we make some comments about the density of positive integers which can be represented as the sum…
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…
We suggest new types and interpretation of complex and hypercomplex numbers for which the commutative, associative, and distributive laws and the norm axioms are trivially satisfied.