Abstract
Throughout this chapter R → S will be a faithfully flat ring extension. If M is an S-module, then M ⊗ R S is an S ⊗ R S-module in two ways, directly and by the twist in S⊗S; that is, (a⊗b)(m⊗s) may be am⊗ bs or bm⊗as. In general these two structures are not Isomorphic; if for instance M = S/I, then the annihilator of M ⊗ S is I ⊗ S in one structure and S⊗ I in the other.
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© 1979 Springer-Verlag New York Inc.
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Waterhouse, W.C. (1979). Descent Theory Formalism. In: Introduction to Affine Group Schemes. Graduate Texts in Mathematics, vol 66. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6217-6_17
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DOI: https://doi.org/10.1007/978-1-4612-6217-6_17
Publisher Name: Springer, New York, NY
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