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math.AC2025
Characterization of almost Gorenstein rings in terms of the trace ideal
Ryotaro Isobe, Shinya Kumashiro
We provide a characterization of one-dimensional almost Gorenstein rings in terms of the trace ideal. As an application, we investigate the almost Gorenstein property of certain $\…
math.AC2025
Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings
Shinya Kumashiro, Sora Miyashita
Recent work by Miyashita and Varbaro classified the canonical traces of Stanley--Reisner rings that are Gorenstein on the punctured spectrum, under the Cohen--Macaulay assumption.…
math.AC2025
Full-Trace Modules
Ela Celikbas, Olgur Celikbas, Jürgen Herzog +1
Motivated by the definition of nearly Gorenstein rings, we introduce the notion of full-trace modules over commutative Noetherian local rings--namely, finitely generated modules wh…