Finiteness aspects of Gorenstein homological dimensions

• Autorzy: Samir Bouchiba
• Języki publikacji: EN

Abstrakty

EN

We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R), leftspli(R), recovering a recent theorem of [I. Emmanouil, J. Algebra 372 (2012), 376-396]. Moreover, this formula permits to recover the main theorem of [D. Bennis and N. Mahdou, Proc. Amer. Math. Soc. 138 (2010), 461-465]. Furthermore, we prove that, in the setting of a left and right Noetherian ring, the Gorenstein global dimension is left-right symmetric, generalizing a theorem of Enochs and Jenda. Finally, using recent work of I. Emmanouil and O. Talelli, we compute the Gorenstein global dimension for various types of rings such as commutative ℵ₀-Noetherian rings and group rings.

Kategorie tematyczne

• 13D02: Syzygies, resolutions, complexes
• 16E10: Homological dimension
• 13D05: Homological dimension
• 16E05: Syzygies, resolutions, complexes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 2
• Strony: 171-193

Daty

wydano

2013

Twórcy

autor

Samir Bouchiba

• Department of Mathematics, University Moulay Ismail, Meknes, Morocco

Identyfikatory

DOI

10.4064/cm131-2-2