Related papers: Universal Algebra in UniMath
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Let $\mathfrak{g}$ be a finite dimensional complex simple classical Lie superalgebra and $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. In this paper we define an integral form for the universal enveloping algebra…
The Agda Universal Algebra Library (UALib) is a library of types and programs (theorems and proofs) we developed to formalize the foundations of universal algebra in dependent type theory using the Agda programming language and proof…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
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…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We introduce superequivalence and superuniform spaces.
In this paper, we enlarge the language of MTL-algebras by a unary operation $\forall$ equationally described so as to abstract algebraic properties of the universal quantifier "for any" in its original meaning. The resulting class of…
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
We generalise the $\eta$ regularisation scheme in order to develop a framework for systematically studying regularisation of loops in quantum field theory. This allows us to "solve" a set of gauge consistency conditions for families of…
Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…
Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the closed convex hulls of joint unitary orbits are completely…
In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…
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…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
We provide a general, unified, framework for external zonotopal algebra. The approach is critically based on employing simultaneously the two dual algebraic constructs and invokes the underlying matroidal and geometric structures in an…