FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS

FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS

Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂R M∗ → HomR(HomR(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and ExtiR(M, M) = 0 (i ⩾ 1), then M is projective.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Taehan Suhakhoe hoebo 2020, 57(3), , pp.803-813
Hauptverfasser: Hu, Kui, Lim, Jung Wook, Xing, Shiqi
Format: Artikel
Sprache:eng
Schlagworte:
수학
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M⨂R M∗ → HomR(HomR(M, M), R) is a surjective homomorphism. Particularly, if G-gldim(R) ⩽ ∞ and ExtiR(M, M) = 0 (i ⩾ 1), then M is projective.
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b190531