Almost Gorenstein rings arising from fiber products

Abstract

AbstractThe 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 ringsR,Sof the same dimension$d>0$over a regular local ringTwith$\dim T=d-1$is an almost Gorenstein ring if and only if so areRandS. In addition, the other generalizations of Gorenstein properties are also explored.