TENSOR PRODUCTS OF <i>d</i> -FOLD MATRIX FACTORIZATIONS

Abstract Consider a pair of elements f and g in a commutative ring Q . Given a matrix factorization of f and another of g , the tensor product of matrix factorizations, which was first introduced by Knörrer and later generalized by Yoshino, produces a matrix factorization of the sum $f+g$ . We will study the tensor product of d -fold matrix factorizations, with a particular emphasis on understanding when the construction has a non-trivial direct sum decomposition. As an application of our results, we construct indecomposable maximal Cohen–Macaulay and Ulrich modules over hypersurface domains of a certain form.