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Topologically Algebraic Algebras [PDF]

Mediterranean Journal of Mathematics, 2004
Let \(A\) be a complex topological algebra and \(H(\mathbb{C})\) the algebra of all complex-valued entire functions. An element \(x\) in \(A\) is said to be topologically algebraic if all entire functions operate in \(A\) at the point \(x\) and if there exists a nonzero entire function \(f\) in \(H(\mathbb{C})\) such that \(f(x)=0\).
Abdelbaki Attioui, Rachid Choukri
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Geometric Algebra

Advanced Calculus Fundamentals of Mathematics, 2019
algebra is the study of algebraic structures and include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of ...
Dr Chris Doran
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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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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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HOMOLOGICAL ALGEBRA

Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34, 2021
Anthony Baraconi
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Algebras and Duality (Tensor Algebra, Grassmann Algebra, Clifford Algebra, Lie Algebra) [PDF]

, 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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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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Topics in algebra

AMS/MAA Textbooks, 2021
I. Herstein, Rakesh Balhara
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Matrix Analysis and Applied Linear Algebra

, 2000
C. D. Meyer
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