An Ansatz is proposed for the heptagon relation, that is, an algebraic imitation of five-dimensional Pachner move 4–3. The formula in question realized terms matrices acting a direct sum one-dimensional linear spaces corresponding to 4-faces.

Let (R; m;k) be a local ring (commutative and Noetherian). We will discuss existence and uniqueness of direct-sum decompositions of nitely generated R-modules. One says that R has nite CM type provided there are only nitely many indecomposable maximal Cohen-Macaulay R-modules up to isomorphism. Among complete equicharacteristic hypersurface rings with k algebraically closed of characteristic 6 ...