The Binomial Theorem for Algebraic Structures

Christoph Schwarzweller

University of T\"ubingen

Summary.

In this paper we prove the well-known binomial theorem for algebraic structures. In doing so we tried to be as modest as possible concerning the algebraic properties of the underlying structure. Consequently, we proved the binomial theorem for ``commutative rings'' in which the existence of an inverse with respect to addition is replaced by a weaker property of cancellation.

This work has been partially supported by CALCULEMUS grant HPRN-CT-2000-00102.

MML Identifier: BINOM

Contents (PDF format)

1. Preliminaries
2. On Finite Sequences
3. On Powers in Rings
4. On Natural Products in Rings
5. The Binomial Theorem

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