ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Enclosed binary operation
Groupoid
Ringoid
Semiring
Ring
Multiplicative group
Multiplicative monoid
Multiplicative semigroup
Multiplicative groupoid
Multiplicative binary operation
Natural number multiplication operation
Definition D608
Integer multiplication operation
Formulation 0
Let $\mathbb{Z}$ be the D367: Set of integers.
Let $+$ be the D637: Natural number addition operation.
Let $\cdot$ be the D638: Natural number multiplication operation.
The integer multiplication operation is the D554: Binary operation \begin{equation} \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a c + b d, a d + b c)] \end{equation}
Formulation 1
Let $\mathbb{Z}$ be the D367: Set of integers.
Let $+$ be the D637: Natural number addition operation.
Let $\cdot$ be the D638: Natural number multiplication operation.
The integer multiplication operation is the D554: Binary operation \begin{equation} \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}, \quad [(a, b)] [(c, d)] = [(a \cdot c + b \cdot d, a \cdot d + b \cdot c)] \end{equation}
Children
Rational multiplication operation