20/08/19 16:03:33 bglsLP4c.net
つづき
URLﾘﾝｸ(www.sciencedirect.com)
ScienceDirect
Commutative Field
Handbook of Algebra
Udo Hebisch, Hanns Joachim Weinert, in Handbook of Algebra, 1996
Example 1.7
a)
Clearly, each ring is a semiring and each (not necessarily commutative) field is a semifield.
As usual, we denote by (Z, +, ・) the ring of integers and by (Q, +, ・) and (R, +, ・) the fields of rational and real numbers.
URLﾘﾝｸ(en.wikipedia.org)(mathematics)
Field (mathematics)
Classic definition
・Commutativity of addition and multiplication: a + b = b + a, and a ・ b = b ・ a.
URLﾘﾝｸ(math.uni.lu)
Field Theory by Wulf-Dieter Geyer, Universit¨at Erlangen-Nurnberg ¨
Winter School on Galois Theory
Luxembourg, 15?24 February 2012
Contents
2. Historical remarks about the concept of field . . . . . . . . . . . .. . . 10
2.1. What Wikipedia says . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2. New Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13
2.3. The Birth of the Concept of Field and its Notations . . . . . . . . . . 14
2.4. The Paper of Steinitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
つづく