Subdirectly irreducible algebra

A subdirectly irreducible algebra is a concept from universal algebra, a branch of mathematics that studies algebraic structures. Specifically, an algebraic structure (such as a group, ring, or lattice) is called subdirectly irreducible if it cannot be represented as a non-trivial subdirect product of other algebras. ### Definition An algebra \( A \) is said to be subdirectly irreducible if: 1. It is non-trivial, i.