Results 171 to 180 of about 273,669 (207)
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A Jordan Algebra of a Mal’tsev Algebra
Journal of Mathematical Sciences, 2023This study generalizes the Jordan algebra of a Lie algebra and the existing results on the local finite-dimensionality of Lie PI-algebras with an algebraic adjoint representation to Mal'tsev algebras. It illustrates that Jordan algebras of a Mal'tsev algebra inherit nondegeneracy and strong primeness.
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Algebras with Identical Algebraic Sets
Algebra and Logic, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS
Mathematics of the USSR-Sbornik, 1985This paper contains a complete proof of the following theorem. Let \(\alpha\neq 0,1\) be algebraic, let \(\beta\) be algebraic of degree \(d\geq 2\), and let t be the transcendence degree over \({\mathbb{Q}}\) of the field generated by the numbers (*) \(\alpha^{\beta},...,\alpha^{\beta^{d- 1}}\).
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An Algebra Related To the Algebra of Octaves Or Cayley Algebra
Journal of the London Mathematical Society, 1965The author considers an eight-dimensional algebra over an arbitrary commutative field \(K\). If \(K\) is a field in which \(-1\) is a square, this algebra is isomorphic with the ordinary Cayley algebra over \(K\). Over the field in which \(-1\) is not a square, the two algebras are not all the same. In no case it is a division algebra.
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The Measure Algebra as an Operator Algebra
Canadian Journal of Mathematics, 1968In § I, it is shown that M(G)*, the space of bounded linear functionals on M(G), can be represented as a semigroup of bounded operators on M(G).Let △ denote the non-zero multiplicative linear functionals on M(G) and let P be the norm closed linear span of △ in M(G)*.
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On Polynomial Algebras and Free Algebras
Canadian Journal of Mathematics, 1968It is well known that given the polynomial algebra (for definitions, see §2), an algebra of type τ, and a sequence a of elements of , one can define a congruence relation θa of such that the factor algebra is isomorphic to the subalgebra of generated by a, and the isomorphism is given in a very simple way.
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Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra)
2011Operator algebras play a fundamental role in algebraic quantum field theory. In order to understand this, one has first to understand the crucial algebraic structures of the Euclidean space. The point is that relevant products possess an invariant meaning, that is, they are independent of the choice of a basis of the Euclidean space.
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International Journal of Foundations of Computer Science, 1992
We assume the reader has some familiarity with theories and iteration theories. The main topic of the paper is properties of varieties of iteration algebras. After a preliminary section which contains all of the necessary definitions, we spend some time on a coproduct construction which is needed to prove a fundamental lemma: for each iteration theory
Stephen L. Bloom, Zoltán Ésik
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We assume the reader has some familiarity with theories and iteration theories. The main topic of the paper is properties of varieties of iteration algebras. After a preliminary section which contains all of the necessary definitions, we spend some time on a coproduct construction which is needed to prove a fundamental lemma: for each iteration theory
Stephen L. Bloom, Zoltán Ésik
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ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY
International Journal of Geometric Methods in Modern Physics, 2008We give the definition of algebraic entropy, which is a global index of complexity for dynamical systems with a rational evolution. We explain its geometrical meaning, and different methods, heuristic or exact to calculate this entropy. This quantity is a very good integrability detector.
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Algebraic extensions of prime algebras and algebras of quotients
1986Summary: Let F be a field, \(R\supset B\) be F-algebras such that for every element \(x\in R\) there is a polynomial f(t) with f(x)\(\in B\). The following results are proved: If R is prime and has no nonzero algebraic one-sided ideals, then B is prime with no nonzero algebraic one-sided ideals; if moreover R is noncommutative, then the algebras of ...
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