Related papers: Families of algebraic structures
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…
An introduction to the applications of algebraic surgery to the structure theory of high-dimensional topological manifolds.
Information algebra is algebraic structure for local computation and inference. Given an initial universe set and a parameter set, we show that a soft set system over them is an information algebra. Moreover, in a soft set system, the…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure.
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.
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also…
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
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…
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.…
We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.