Related papers: Logarithms Over a Real Associative Algebra
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the…
We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
Motivated by the classical correspondence between short exact sequences and splitting properties in module theory, this paper examines the projective and injective analogues within the category of Lie algebras. We first show that no Lie…
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
Ordinary algebra of formal power series in one variable is convenient to study by means of the algebra of Riordan matrices and the Riordan group. In this paper we consider algebra of formal power series without constant term, isomorphic to…
Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…
Fork algebras are an extension of relation algebras obtained by extending the set of logical symbols with a binary operator called fork. This class of algebras was introduced by Haeberer and Veloso in the early 90's aiming at enriching…
A further significant extension is presented of the infinitely large class of differential algebras of generalized functions which are the basic structures in the nonlinear algebraic theory listed under 46F30 in the AMS Mathematical Subject…
Given a chiral algebra, we study modules over an arbitrary power of a curve. We describe this category in three different ways: in terms of factorization, in terms of certain chiral operations and as modules for a lie algebra in a certain…
We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of their relevance to kinematics and mechanism science, we put…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Implicative algebras, recently discovered by Miquel, are combinatorial structures unifying classical and intuitionistic realizability as well as forcing. In this paper we introduce implicative assemblies as sets valued in the separator of…
In this article, I introduce a group-theoretical method to prove positivity of certain linear combinations (with coefficients generally lying in $\mathbb{C}$) of exponential functions under a set of semidefinite linear constraints. The…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…