Lie rings and Lie algebras with ideal spreads are abelian or of rank 2 (Q1306490)

A spread of a Lie ring \(L\) is a partition \(\mathcal S\) of \(L\) into mutually complementary Lie subrings. The spread is called ideal if the commutator of any \(x \in L\) and any \(U \in \mathcal S\) is contained in an element of \(\mathcal S\). The author shows that a nonabelian Lie ring which possesses an ideal spread can be naturally seen as a two-dimensional Lie algebra over some field \(K\) such that the spread elements are just the 1-dimensional \(K\)-subspaces.