Algebra with weak distributivity (Q761477)

An algebraic structure is sought to explain the similarities between the theories of semiprime rings and lattice-ordered groups. In addition, considerable pains are taken to produce an economical ''umbrella'' structure. This is accomplished with reasonable success with the r- groups, which at least subsume all abelian lattice-ordered groups and all commutative regular rings. The main theorem is a decomposition result which breaks up an r-group into three pieces: a lattice-ordered group, a commutative regular ring and an algebra of characteristic three.