On the embedding of universal algebras in groupoids holding the law $XY\ast ZU\ast \ast = XZ\ast YU\ast \ast $

M. D. Radojčić

Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law $X Y * Z U * * = X Z * Y U * *$ ”

Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

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Given a groupoid $〈 G, ☆ 〉$ , and $k \geq 3$ , we say that $G$ is antiassociative if an only if for all $x_{1}, x_{2}, x_{3} \in G$ , $(x_{1} ☆ x_{2}) ☆ x_{3}$ and $x_{1} ☆ (x_{2} ☆ x_{3})$ are never equal. Generalizing this, $〈 G, ☆ 〉$ is $k$ -antiassociative if and only if for all $x_{1}, x_{2}, ..., x_{k} \in G$ , any two distinct expressions made by putting parentheses in $x_{1} ☆ x_{2} ☆ x_{3} ☆ \dots ☆ x_{k}$ are never equal. We prove that for every $k \geq 3$ , there exist finite groupoids that are $k$ -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

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On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

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Universal lifting theorem and quasi-Poisson groupoids

David Inglesias-Ponte, Camille Laurent-Gengoux, Ping Xu (2012)

Journal of the European Mathematical Society

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We prove the universal lifting theorem: for an $α$ -simply connected and $α$ -connected Lie groupoid $Γ$ with Lie algebroid $A$ , the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative multi-vector fields on $Γ$ . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids....

Algebraic Superconnections, $S U (2 ∣ 1)$ and Electroweak Interactions

R. Coquereaux (1992)

Recherche Coopérative sur Programme n°25

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Universal embeddings of $l^{1} (α)$ into the space of continuous functions on a product space

N. Kalamidas, Th. Zachariades (1989)

Colloquium Mathematicae

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Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

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Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

N. Ch. Wass

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This thesis is concerned with the problem of determining a measure of algebraic independence for a particular m-tuple θ₁,..., $θ_{m}$ of complex numbers. Specifically, let K be a number field and let f₁(z),..., $f_{m} (z)$ be elements of K[[z]] algebraically independent over K(z) satisfying equations of the form(*) $f_{j} (z^{b}) = \sum_{i = 1}^{m} f_{i} (z) a_{i j} (z) + b_{j} (z)$ (j = i,...,m)for b ≥ 2, $a_{i j} (z)$ , $b_{j} (z)$ in K(z). Suppose finally that α ∈ K is such that 0 < |α| < 1, the $f_{j} (z$ ) converge at z = α and the $a_{i j} (z)$ , $b_{j} (z)$ are analytic at $z = α, α^{b}, α^{b ²}, . . .$ Then the $θ_{i} = f_{i} (α)$ are algebraically independent...

On the number of finite algebraic structures

Erhard Aichinger, Peter Mayr, R. McKenzie (2014)

Journal of the European Mathematical Society

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We prove that every clone of operations on a finite set $A$ , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting $R$ for some finitary relation $R$ over $A$ . It follows that for a fixed finite set $A$ , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...

Multiplicatively dependent triples of Tribonacci numbers

Carlos Alexis Ruiz Gómez, Florian Luca (2015)

Acta Arithmetica

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We consider the Tribonacci sequence $T : = {T_{n}}_{n \geq 0}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_{n + 3} = T_{n + 2} + T_{n + 1} + T_{n}$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.

A representation theorem for tense $n \times m$ -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo, Gustavo Pelaitay (2015)

Mathematica Bohemica

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In 2000, Figallo and Sanza introduced $n \times m$ -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$ -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class $_{n \times m}$ of tense $n \times m$ -valued Łukasiewicz-Moisil algebras (or tense LM $_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense...

A generalization of a formalized theory of fields of sets on non-classical logics

Helena Rasiowa

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Contents Introduction.................................................................................................................................................. 3 § 1. System $𝒮$ of a propositional calculus...................................................................... 4 § 2. System $𝒮 *$ ..................................................................................................................... 5 § 3. $𝒮 *$ -algebras.....................................................................................................................

$A F$ -algebras and topology of mapping tori

Igor Nikolaev (2015)

Czechoslovak Mathematical Journal

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The paper studies applications of $C^{*}$ -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of $A F$ -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding $A F$ -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension $2$ , $3$ and $4$ . In conclusion, we consider two numerical examples illustrating our main results.

Trivialization of $𝒞 (X)$ -algebras with strongly self-absorbing fibres

Marius Dadarlat, Wilhelm Winter (2008)

Bulletin de la Société Mathématique de France

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Suppose $A$ is a separable unital $𝒞 (X)$ -algebra each fibre of which is isomorphic to the same strongly self-absorbing and $K_{1}$ -injective $C^{*}$ -algebra $𝒟$ . We show that $A$ and $𝒞 (X) \otimes 𝒟$ are isomorphic as $𝒞 (X)$ -algebras provided the compact Hausdorff space $X$ is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.

Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

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We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime $p$ the reduction modulo $p$ of the diagonal of a multivariate algebraic power series $f$ with integer coefficients is an algebraic power series of degree at most $p^{A}$ and height at most $A p^{A}$ , where $A$ is an effective constant that only...

The moduli space of commutative algebras of finite rank

Bjorn Poonen (2008)

Journal of the European Mathematical Society

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The moduli space of rank- $n$ commutative algebras equipped with an ordered basis is an affine scheme $𝔅_{n}$ of finite type over $ℤ$ , with geometrically connected fibers. It is smooth if and only if $n \leq 3$ . It is reducible if $n \geq 8$ (and the converse holds, at least if we remove the fibers above $2$ and $3$ ). The relative dimension of $𝔅_{n}$ is $\frac{2}{27} n^{3} + O (n^{8 / 3})$ . The subscheme parameterizing étale algebras is isomorphic to ${GL}_{n} / S_{n}$ , which is of dimension only $n^{2}$ . For $n \geq 8$ , there exist algebras that are not limits of étale algebras. The dimension...

A Dichotomy Principle for Universal Series

V. Farmaki, V. Nestoridis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Applying results of the infinitary Ramsey theory, namely the dichotomy principle of Galvin-Prikry, we show that for every sequence ${(α_{j})}_{j = 1}^{\infty}$ of scalars, there exists a subsequence ${(α_{k_{j}})}_{j = 1}^{\infty}$ such that either every subsequence of ${(α_{k_{j}})}_{j = 1}^{\infty}$ defines a universal series, or no subsequence of ${(α_{k_{j}})}_{j = 1}^{\infty}$ defines a universal series. In particular examples we decide which of the two cases holds.

Embedding in $T_{3}$ - $F_{σ}$ spaces

D. W. Hajek, I. Irizarry (1981)

Matematički Vesnik

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Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law X Y * Z U * * = X Z * Y U * * ”

Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law $X Y * Z U * * = X Z * Y U * *$ ”