Related papers: Unital algebra structure and generalized algebra n…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We present an ongoing effort to implement Universal Algebra in the UniMath system. Our aim is to develop a general framework for formalizing and studying Universal Algebra in a proof assistant. By constituting a formal system for isolating…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm on it. Let A be a uniform topological algebra whose spectrum…
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
This paper provides an extensive study of the homotopy theory of types of algebras with units, like unital associative algebras or unital commutative algebras for instance. To this purpose, we endow the Koszul dual category of curved…
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$. We…