Related papers: G\"odel algebras: interactive dualities and their …
We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete…
This paper presents a new method for obtaining small algebras to check the admissibility-equivalently, validity in free algebras-of quasi-identities in a finitely generated quasivariety. Unlike a previous algebraic approach of Metcalfe and…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
The choice of an isomorphism, a duality, between a finite abelian group $A$ and its character group allows one to define dual codes of additive codes over $A$. Properties of dualities and dual codes are studied, continuing work of Delsarte…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the…
This paper presents a systematic study of coproducts. This is carried out principally, but not exclusively, for finitely generated quasivarieties A that admit a (term) reduct in the variety D of bounded distributive lattices. In this…
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with…
We investigate a natural Heyting algebra structure on the set of Dyck paths of the same length. We provide a geometrical description of the operations of pseudocomplement and relative pseudocomplement, as well as of regular elements. We…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual.
We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…
Given a finitely generated free monoid $X$ and a morphism $\phi : X\to X$, we show that one can construct an algebra, which we call an iterative algebra, in a natural way. We show that many ring theoretic properties of iterative algebras…
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
Translation association schemes are constructed from actions of finite groups on finite abelian groups satisfying certain natural conditions. It is also shown that the mere existence of maps from finite groups to themselves sending each…
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…