Almost Gorenstein rings arising from fiber products
Naoki Endo, Shirô Gotô, Ryotaro Isobe
Abstract
Abstract The purpose of this paper is, as part of the stratification of Cohen–Macaulay rings, to investigate the question of when the fiber products are almost Gorenstein rings. We show that the fiber product $R \times _T S$ of Cohen–Macaulay local rings R , S of the same dimension $d>0$ over a regular local ring T with $\dim T=d-1$ is an almost Gorenstein ring if and only if so are R and S . In addition, the other generalizations of Gorenstein properties are also explored.
Topics & Concepts
MathematicsLocal ringFiberDimension (graph theory)Pure mathematicsStratification (seeds)Ring (chemistry)Product (mathematics)CombinatoricsDiscrete mathematicsGeometryComposite materialMaterials scienceDormancyGerminationBiologyBotanyOrganic chemistrySeed dormancyChemistryCommutative Algebra and Its ApplicationsAlgebraic structures and combinatorial modelsAlgebraic Geometry and Number Theory