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Fecha de fin
Resumen: Avramov and Foxby introduced two different notions of homological dimensions for unbounded complexes: the injective dimension (id) is defined using dg-injective resolutions, while the graded injective dimension (gr-id) is defined using degreewise injective resolutions. In general, gr-id X is less than or equal to id X, for any complex X. Avramov and Foxby showed that equality holds whenever the ring has finite global dimension, and asked if the converse is true. In joint work with Iyengar we answered their question in the affirmative in the case of noetherian rings. More precisely, we showed that if R is noetherian then gr-id X = id X for any complex X if and only if R is regular.
In recent work with Gillespie we extend the result from noetherian to coherent rings, by proving that a coherent ring R is regular if and only the injective dimension of any complex X agrees with its graded injective dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, projective R-modules, and respectively flat R-modules.
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Viernes 23/5 a las 11:15
Salón de Seminarios del IMERL y a través de Zoom
Contacto: Dalia Artenstein darten [at] fing.edu.uy (darten[at]fing[dot]edu[dot]uy) Rafael Parra rparra [at] fing.edu.uy (rparra[at]fing[dot]edu[dot]uy)
Información de acceso a Zoom / Zoom access info:
Enlace / link: https://salavirtual-
ID de reunión / Meeting ID: 850 0131 1823