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Almost Gorenstein rings arising from fiber products
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 2 / June 2021
- Published online by Cambridge University Press:
- 10 July 2020, pp. 383-400
- Print publication:
- June 2021
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- Article
- Export citation
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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.
