SAMS Subject Classification Number: 4

A noetherian form is a self-dual axiomatic context in which the Noether isomorphism theorems can be established. A noetherian form consists of objects, morphisms between objects and subobject lattices for each object. By design, any group-like variety together with its homomorphisms and subalgebra lattices is a noetherian form. In this talk we will show that even though a non-group-like variety together with its homomorphisms and subalgebra lattices is not a noetherian form, the subalgebra lattices can be suitably extended such that we have a noetherian form. The construction of these noetherian forms over a variety can be described categorically. The main result in this talk, is a characterization of when this more general categorical construction results noetherian form.