Decompositions of homomorphisms
Definability for equational theories of commutative groupoids
We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.
Disjoint and complete unions of incidence structures
Some decompositions of general incidence structures with regard to distinguished components (modular or simple) are considered and several structure theorems for them are deduced.
Disjoint unions of incidence structures and complete lattices