On the non-commutative Newton binomial formula
A. Hosseini, M. Mohammadzadeh Karizaki
TL;DR
This paper presents a straightforward proof of the non-commutative Newton binomial formula in unital and non-unital algebras, extending it to negative powers using generalized derivations.
Contribution
It introduces a simple proof method for the non-commutative Newton binomial formula and extends it to non-unital algebras and negative powers.
Findings
Proof of the non-commutative Newton binomial formula in unital algebras
Extension of the formula to non-unital algebras
Derivation of the formula for negative powers
Abstract
In this article, using generalized derivations, we obtain a simple idea to prove the non-commutative Newton binomial formula in unital algebras and then, we extend that formula to non-unital algebras. Additionally, we establish the non-commutative Newton binomial formula with a negative power.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms