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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
over a regular local ring T with
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.
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