Definition:Algebra over Field/Multiplication
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Definition
Let $F$ be a field.
Let $\struct {A, *}$ be an algebra over $F$ such that:
- $A$ is a vector space over $F$
- $* : A^2 \to A$ is a bilinear mapping.
The bilinear mapping $*$ is often referred to as multiplication.
Also see
- Results about algebras over fields can be found here.
Sources
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- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebra over field
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): algebra: 1.