Algebra A is subdirectly-irreducible iff intersection of non-trivial congruences is non-trivial. Birkhoff: every algebra is subdirect product of subdirectly-irreducibles. Foundational decomposition theorem in universal algebra.
Algebra A is subdirectly-irreducible iff intersection of non-trivial congruences is non-trivial. Birkhoff: every algebra is subdirect product of subdirectly-irreducibles. Foundational decomposition theorem in universal algebra.