Results 271 to 280 of about 34,528,690 (304)

ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

Mathematics of the USSR-Sbornik, 1985
This 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, 1965
The 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, 1968
In § 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, 1968
It 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)

2011
Operator 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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ITERATION ALGEBRAS

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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ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY

International Journal of Geometric Methods in Modern Physics, 2008
We 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

1986
Summary: 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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The C*-Algebra of a Function Algebra

Integral Equations and Operator Theory, 2003
The author considers the pair \((A,G)\) where \(G\) is a compact Hausdorff space and \(A\) is a function algebra on \(G\), i.e., \(A\) is a norm-closed (proper) subalgebra of \(C(G)\), the unital C*-algebra of continuous complex-functions on \(G\) separating the points of \(G\).
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Algebraic Lie Algebras

The Annals of Mathematics, 1947
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