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The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension

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  • Khaled Alhazmy
  • Fuad Ali Ahmed Almahdi
  • Younes El Haddaoui
  • Najib Mahdou
  • R. Sundareswaran

Abstract

The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring R with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of R is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.

Suggested Citation

  • Khaled Alhazmy & Fuad Ali Ahmed Almahdi & Younes El Haddaoui & Najib Mahdou & R. Sundareswaran, 2024. "The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension," Journal of Mathematics, Hindawi, vol. 2024, pages 1-7, April.
    • Handle: RePEc:hin:jjmath:4896819
    DOI: 10.1155/2024/4896819
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