Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

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

The terminology and notation used in this paper have been introduced in the following articles [12] [6] [17] [13] [2] [4] [5] [1] [16] [18] [3] [10] [7] [8] [15] [9] [14] [11]

Contents (PDF format)

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

Bibliography

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[12] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[13] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[14] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[15] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[16] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[17] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
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Received November 20, 2000


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