Note on the Kurosch-Ore Theorem
R. P. Dilworth · Birkhäuser Boston eBooks · 1990
The Kurosch-Ore theorem 1 asserts that if an element of a modular lattice has two decompositions into irreducibles, then each irreducible of one decomposition may be replaced by a suitably chosen irreducible from the other decomposition. It follows that the number of irreducibles in the two decompositions is the same.