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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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Algebraic radicals and incidence algebras
Journal of Discrete Mathematical Sciences and Cryptography, 1999Let \(I(X,R)\) 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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Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34, 2021
Anthony Baraconi
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Anthony Baraconi
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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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THE MULTIPLIER ALGEBRA OF A BEURLING ALGEBRA
Bulletin of the Australian Mathematical Society, 2014AbstractFor a discrete abelian cancellative semigroup$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$with a weight function$\omega $and associated multiplier semigroup$M_\omega (S ...
Bhatt, S. J. +2 more
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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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The C*-Algebra of a Function Algebra
Integral Equations and Operator Theory, 2003The 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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