Displaying similar documents to “Affine completeness of de Morgan algebras”

Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus

Frederick M. Goodman, Holly Hauschild (2006)

Fundamenta Mathematicae

Similarity:

The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.

The algebra of mode homomorphisms

Kira Adaricheva, Anna Romanowska, Jonathan Smith (2014)

Open Mathematics

Similarity:

Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary...

Remarks on affine complete distributive lattices

Dominic Zypen (2006)

Open Mathematics

Similarity:

We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that the class of affine complete bounded distributive lattices is closed under products and free products. We show that every (not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in the class of affine complete lattices.

Affine ultraregular generalized functions

Khaled Benmeriem, Chikh Bouzar (2010)

Banach Center Publications

Similarity:

Algebras of ultradifferentiable generalized functions satisfying some regularity assumptions are introduced. We give a microlocal analysis within these algebras related to the affine regularity type and the ultradifferentiability property. As a particular case we obtain new algebras of Gevrey generalized functions.

Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two

Tomasz Brzeziński (2015)

Colloquium Mathematicae

Similarity:

Two-dimensional integrable differential calculi for classes of Ore extensions of the polynomial ring and the Laurent polynomial ring in one variable are constructed. Thus it is concluded that all affine pointed Hopf domains of Gelfand-Kirillov dimension two which are not polynomial identity rings are differentially smooth.

Flocks in universal and Boolean algebras

Gabriele Ricci (2010)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns...

A glimpse of deductive systems in algebra

Dumitru Buşneag, Sergiu Rudeanu (2010)

Open Mathematics

Similarity:

The concept of a deductive system has been intensively studied in algebraic logic, per se and in connection with various types of filters. In this paper we introduce an axiomatization which shows how several resembling theorems that had been separately proved for various algebras of logic can be given unique proofs within this axiomatic framework. We thus recapture theorems already known in the literature, as well as new ones. As a by-product we introduce the class of pre-BCK algebras. ...

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

Similarity:

Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

Similarity:

An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.