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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 × 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. 2010 Mathematics Subject Classification. 13H10, 13H15, 18A30.doi:10.4153/s000843952000051x fatcat:frkwkcwxlzdfbkol6oy3xus344