Geodesic
Flat cotorsion modules over Noether algebras
Documenta mathematica, Tome 27 (2022), pp. 1101-1167
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For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable injective left modules and the isoclasses of indecomposable flat cotorsion right modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality of Ziegler spectra.
DOI : 10.4171/dm/893
Classification : 13B35, 16D40, 16D70, 16G30
Mots-clés : flat cotorsion module, Noether algebra, pure-injective module, Ziegler spectrum, elementary duality, ideal-adic completion 
@article{10_4171_dm_893,
     author = {Tsutomu Nakamura and Ryo Kanda},
     title = {Flat cotorsion modules over {Noether} algebras},
     journal = {Documenta mathematica},
     pages = {1101--1167},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/893},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/893/}
}
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Tsutomu Nakamura; Ryo Kanda. Flat cotorsion modules over Noether algebras. Documenta mathematica, Tome 27 (2022), pp. 1101-1167. doi: 10.4171/dm/893

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