Hausdorff Analytic Functions in a Three-Dimensional Associative Noncommutative Algebra

Hausdorff-analytic Functions of Matrices1

Noncommutative Algebra

1. Basics 2 1.1. Commutants 2 1.2. Opposite Rings 3 1.3. Units 3 1.4. Ideals 4 1.5. Modules 4 1.6. Division rings 5 1.7. Endomorphism rings 7 1.8. Monoid Rings 8 1.9. Noetherian and Artinian Rings 11 1.10. Simple rings 15 1.11. Prime ideals and prime rings 17 1.12. Notes 18 2. Wedderburn-Artin Theory 18 2.1. Semisimple modules and rings 18 2.2. Wedderburn-Artin I: Semisimplicity of Mn(D) 20 2.3...

The primitives of the Hopf algebra of noncommutative symmetric functions

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theore...

Every Simple Higher Dimensional Noncommutative Torus Is an at Algebra

We prove that every simple higher dimensional noncommutative torus is an AT algebra.

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.