Related papers: On associative operations on commutative integral …
We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.
We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the…
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case…
We study commutative associative polynomial operations $\mathbb{A}^n\times\mathbb{A}^n\to\mathbb{A}^n$ with unit on the affine space $\mathbb{A}^n$ over an algebraically closed field of characteristic zero. A classification of such…
We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or…
In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the $k$-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A…
We prove several fundamental results about divisorial integral domains in the setup of multiplicative lattices.
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
Analogs of Laguerre and Meixner orthogonal polynomials in the algebra of symmetric functions are studied. This is a detailed exposition of part of the results announced in arXiv:1009.2037. The work is motivated by a connection with a model…
We define a class of associative algebras generalizing 'clannish algebras', as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well known 'string…
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…
The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…
We study functions defined on a closed segment of the real line that belong to the class of Gonchar. We show that the graphs of such functions are pluripolar. We also discuss the generalizations of our result to functions defined on a…
A classification of commutative integral domains consisting of ordinary differential operators with matrix coefficients is established in terms of morphisms between algebraic curves.
This paper is an attempt to unify the multivariable operator model theory for ball-like domains and commutative polydiscs, and extend it to a more general class of noncommutative polydomains. An important role in our study is played by…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that…
Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping…