 A notable example is a Lie algebra.There exists some structure theory for such algebras that generalizes the analogous results for Lie algebras and associative algebras.A semiring (sometimes "rig") is obtained by weakening the assumption that ("R", +) is an abelian group to the assumption that ("R", +) is a commutative monoid, and adding the axiom that 0 · "a" = "a" · 0 = 0 for all "a" in "R" (since it no longer follows from the other axioms).