Results 281 to 290 of about 24,201,802 (317)

Algebras with Identical Algebraic Sets

Algebra and Logic, 2015
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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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HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS

Bulletin of the Australian Mathematical Society, 2014
AbstractLet$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K$be a locally compact hypergroup endowed with a left Haar measure and let$L^1(K)$be the usual Lebesgue space of$K$with respect ...
Maghsoudi, S., Seoane-Sepúlveda, J. B.
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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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Algebraic radicals and incidence algebras

Journal of Discrete Mathematical Sciences and Cryptography, 1999
Let \(I(X,R)\) denote the incidence algebra of the locally finite partially ordered set \(X\) over the ring \(R\) (with identity). The objective of this paper is to describe the elements in the upper nilradical of \(I(X,R)\). Any \(f\in I(X,R)\) can be decomposed as \(f=f_D+f_U\) where \(f_D(x,x)=f(x,x)\) and \(f_U(x,y)=f(x,y)\) for \(x\neq y\) in \(X\)
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Bourgain Algebras of Douglas Algebras

Canadian Journal of Mathematics, 1992
Let A be a Banach algebra and let B be a linear subspace of A. Recall that A has the Dunford Pettis property if whenever ƒn→ 0 weakly in A* and φn → 0 weakly in A* then φn(ƒn) → 0. Bourgain showed that H∞ has the Dunford Pettis property using the theory of ultraproducts.
Mortini, Raymond, Gorkin, Pamela, Izuchi, K.   +2 more
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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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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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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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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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