The $\phi$-weak dimension of $\phi$-pseudo-valuation rings

Authors

  • Hwankoo Kim Division of Computer Engineering, Hoseo University, Asan, Republic of Korea
  • Najib Mahdou Department of Mathematics, Faculty of Science and Technology of Fez, University S. M. Ben Abdellah Fez, Morocco
  • El Houssaine Oubouhou Department of Mathematics, Faculty of Science and Technology of Fez, University S. M. Ben Abdellah Fez, Morocco

DOI:

https://doi.org/10.3842/umzh.v77i8.8299

Keywords:

$\phi$-weak global dimension, $\phi$-pseudo-valuation ring, pseudo-valuation domain, $\phi$-CR ring, strongly $\phi$-ring

Abstract

UDC 512.5

It is shown that, for a strongly $\phi$-pseudo-valuation ring, which is nonnil-coherent, the only possible values of the $\phi$-weak global dimension are 0, 1, and $\infty.$ We then provide necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coherent. As an application of these findings, we demonstrate that if $R$ is a strongly nonnil-coherent $\phi$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $\phi$-pseudo-valuation ring.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 8, 2025.

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Published

11.09.2025

Issue

Vol. 77 No. 8 (2025)

Section

Research articles