In chapter 2 of Atiyah-Macdonald are introduced the flat modules, and the algebras. However it is not given any definition of flat algebra, while in exercise 5 and 8, for example, is needed. I don't even find anything online; is a flat $A$-algebra just an $A$-algebra that is flat as an $A$-module? It would seem reasonable to me, since the concept of flatness is based on exact sequences (that are defined for modules, not algebras). Thanks in advance for any clarify
2026-03-27 21:55:46.1774648546
Confusion about a definition in Atiyah-Macdonald
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