2. Subdirect representations

Usually we want to use subdirect products ``up to isomorphism''.

2.1 Definition. A subdirect representation of an algebra ${\cal A}$ is an embedding ${\cal A} \hookrightarrow \prod _ {\gamma \in \Gamma} {\cal B} _ \gamma$ whose image is a subdirect product.

For example, a three-element chain (as a distributive lattice) has a subdirect representation as a subdirect product of two two-element chains, as in Figure .

Figure: Subdirect representation of a 3-element chain

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