BASS NUMBERS AND ENDOMORPHISM RINGS OF GORENSTEIN INJECTIVE MODULES

Journal of Commutative Algebra 2026 Open access

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Authors: Reza Sazeedeh
DOI: 10.1216/jca.2026.18.233
Cited by: 0

Abstract

Let R be a commutative noetherian ring admitting a dualizing complex. Let 𝔭 be a prime ideal of R and let G(R/𝔭) be the Gorenstein injective envelope of the R-module R/𝔭. We provide necessary and sufficient conditions under which G(R/𝔭) is an R𝔭-module. We study the Bass numbers of G(R/𝔭) and show that if R/𝔭 has finite Gorenstein injective (projective) dimension, then the Bass numbers of G(R/𝔭) are finite. Finally, we introduce a subring S(𝔭)𝔭 of the endomorphism ring EndR𝔭(G(R𝔭/𝔭R𝔭)) and show that S(𝔭)𝔭 is noetherian containing a commutative noetherian ring.

Fields of Study & Subjects

Algebraic structures and combinatorial models Commutative Algebra and Its Applications Rings Modules and Algebras

Publication details

Journal / source
Journal of Commutative Algebra
Volume
18
Issue
2
Pages
233–250
Publication date
29 July 2026
Language
EN