  This note gives a unifying characterization and exposition of strongly
irreducible elements and their duals in lattices. The interest in the study of
strong irreducibility stems from commutative ring theory, while the dual
concept of strong irreducibility had been used to define Zariski-like
topologies on specific lattices of submodules of a given module over an
associative ring. Based on our lattice theoretical approach, we give a unifying
treatment of strong irreducibility, dualize results on strongly irreducible
submodules, examine its behavior under central localization and apply our
theory to the frame of hereditary torsion theories.
