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ACM Communications in Computer Algebra, 2020
The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees.
Marc Härkönen +3 more
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The Macaulay2 [5] package AlgebraicOptimization implements methods for determining the algebraic degree of an optimization problem. We describe the structure of an algebraic optimization problem and explain how the methods in this package may be used to determine the respective degrees.
Marc Härkönen +3 more
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Algebraic Lie Algebras of Bounded Degree
Journal of Mathematical Sciences, 2021Let \(F\) be an associative and commutative ring with 1, and let \(R\) be an associative algebra over \(F\). Considered with the usual Lie bracket, \(R\) becomes a Lie algebra denoted by \(R^{(-)}\); analogously if \(1/2\in F\), by means of the Jordan product \(a\cdot b=(1/2)(ab+ba)\) it becomes a Jordan algebra denoted by \(R^{(+)}\). Suppose \(R\) is
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Degree of matrix relation algebras
Algebra Universalis, 2002The concept of a basis of degree at least \(N\) for a matrix relation algebra was introduced by R. D. Maddux in 1983. The authors use it to define a relation algebra of degree at least \(N\). It is shown that a relation algebra and its \(n\)-matrix relation algebra have the same degree. An intermediate result relates the degree of a relation algebra to
el Bachraoui, M., van de Vel, M.L.J.
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Algebra Colloquium, 2006
We define a degree stable Lie algebra. Since the special type Lie algebra S+(2) is degree stable, we find the automorphism group Aut Lie (S+(2)) of the Lie algebra S+(2) and prove the Jacobian conjecture of the Lie algebra S+(2).
Nam, Ki-Bong, Choi, Seul Hee
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We define a degree stable Lie algebra. Since the special type Lie algebra S+(2) is degree stable, we find the automorphism group Aut Lie (S+(2)) of the Lie algebra S+(2) and prove the Jacobian conjecture of the Lie algebra S+(2).
Nam, Ki-Bong, Choi, Seul Hee
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Bounded degree of algebraic topological algebras
Communications in Algebra, 1994We give a short proof of theorems of Kaplansky and Slin'ko concerning the bounded degree of certain associative or Jordan algebraic topological algebras. This new proof even works for power-associative algebras.
Bienvenido Cuartero, José E. Galé
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Monadic Algebras with finite degree
Algebra Universalis, 1975A monadic algebraA has finite degreen ifA/M has at most 2n elements for every maximal idealM ofA and this bound is obtained for someM. Every countable monadic algebra with a finite degree is isomorphic to an algebra Γ(X, S) whereX is a Boolean space andS is a subsheaf of a constant sheaf with a finite simple stalk.
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Bounded degree of weakly algebraic topological Lie algebras
manuscripta mathematica, 1993It is known that under some topological conditions, algebraic algebras over a field are necessarily algebraic of bounded degree. A simple proof of this, valid for power-associative algebras is given by \textit{B. Cuartero} and \textit{J. E. Galé} [Commun. Algebra 22, 329-337 (1994; Zbl 0837.17002)].
Cuartero, Bienvenido +3 more
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Structure Theory for Algebraic Algebras of Bounded Degree
The Annals of Mathematics, 1945openaire +2 more sources