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]
-
Preliminaries
-
On Finite Sequences
-
On Powers in Rings
-
On Natural Products in Rings
-
The Binomial Theorem
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Received November 20, 2000
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