Canonical traces of fiber products and their applications

Abstract: We study the canonical trace of the fiber product of Noetherian rings. Furthermore, we extend results on the class of Cohen-Macaulay rings called Teter type to Noetherian rings. As an application of our study on canonical traces and Noetherian rings of Teter type, we compute the canonical trace of the Stanley-Reisner ring arising from a non-connected simplicial complex. In particular, we provide a characterization of Stanley-Reisner rings for which the canonical trace contains the graded maximal ideal, even when the underlying simplicial complex is not connected.