Universal Algebra

up:: 021 MOC Algebra

A universal algebra is a double $(X,\mathcal{F}$, where $X$ is a set, and $\mathcal{F}$ is a collection of $n$-ary functions.

Examples

• A Group $(G,+)$ is a universal algebra, with $\mathcal{F}=\{+:G\times G\to G\}$
• A Field can be thought as a universal algebra $(\mathbb{F},+,\cdot )$, with $\mathcal{F}=\{+:\mathbb{F}\times \mathbb{F}\to \mathbb{F},\cdot :\mathbb{F}\times \mathbb{F}\to \mathbb{F}\}$
• A Lattice is also a universal algebra $(X,\wedge ,\vee )$

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 02