Results 271 to 280 of about 23,180 (297)
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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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Composition Algebras of Arbitrary Degrees
Journal of Mathematical Sciences, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guseva, N. I., Lukyanova, E. V.
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TRU Mathematics, 1986
Let K be a cyclotomic extension of the rational field \({\mathbb{Q}}\). A central simple K-algebra is called a Schur algebra over K if it is isomorphic to a simple component of the group algebra K[G] for some finite group G. The purpose of this paper is to determine the set of all Schur algebras over K for some abelian fields K.
YAMADA, TOSHIHIKO, ITO, SEIICHI
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Let K be a cyclotomic extension of the rational field \({\mathbb{Q}}\). A central simple K-algebra is called a Schur algebra over K if it is isomorphic to a simple component of the group algebra K[G] for some finite group G. The purpose of this paper is to determine the set of all Schur algebras over K for some abelian fields K.
YAMADA, TOSHIHIKO, ITO, SEIICHI
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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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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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Restrictions on the degree spectra of algebraic structures [PDF]
Siberian Mathematical Journal, 2008 We construct the degree b ≤ 0″ admitting no algebraic structure with degree spectrum {x: x ≰ b}. Moreover, we solve Miller's problem of distinguishing incomparable degrees by the spectra of linear orderings.
I Sh Kalimullin
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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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Degree Spectra of Relations on Boolean Algebras
Algebra and Logic, 2003The main result reads as follows: Let \(R\) be a computable relation on a computable Boolean algebra \(B\). Then \(R\) is either definable by a quantifier-free formula with constants, or the set of Turing degrees of its isomorphic images in isomorphic computable copies of \(B\) is infinite.
Goncharov, S. S. +2 more
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The Algebraic Degree of Perfect Binary Codes
IEEE Transactions on Information Theory, 2008Summary: In this communication, we give a complete characterization for the range of the algebraic degree of perfect binary codes. For 1-perfect binary codes, we show that for any \(d\) in the algebraic degree range, there are Vasil'ev codes with algebraic degree \(d\). It is also shown that the algebraic degree of 1-perfect binary codes is independent
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