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On Gorenstein Fiber Products And Applications, Saeed Nasseh, Ryo Takahashi, Keller Vandebogert
On Gorenstein Fiber Products And Applications, Saeed Nasseh, Ryo Takahashi, Keller Vandebogert
Department of Mathematical Sciences Faculty Publications
We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.
Cohen Factorizations: Weak Functoriality And Applications, Saeed Nasseh, Sean Sather-Wagstaff
Cohen Factorizations: Weak Functoriality And Applications, Saeed Nasseh, Sean Sather-Wagstaff
Department of Mathematical Sciences Faculty Publications
We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a “weak functoriality” result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen–Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.
Local Rings Of Embedding Codepth At Most 3 Have Only Trivial Semidualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff
Local Rings Of Embedding Codepth At Most 3 Have Only Trivial Semidualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff
Department of Mathematical Sciences Faculty Publications
We prove that a local ring R of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, R itself and a dualizing R-complex if one exists.