JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

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CRITERIA OF $J$-INDEPENDENCE AND COMPARISON OF THE ANALYTIC SPREAD OF TWO $g$-AXIS-QUASI-GRADUATIONS OF AN $\mathcal{R}$-MODULE $\mathbb{M}$

Authors

  • Kouadjo Pierre BROU
  • Eugène Deval BECHE
  • Laurent Angoua WASSA

Keywords:

axis-quasi-graduation, quasi-graduations, analytic spread, axial sum

DOI:

https://doi.org/10.17654/0972555525037

Abstract

In this work, we first establish the criterion of J-independence of the elements of a module with respect to an axis-quasi-graduation of a module through several propositions and theorems. Then, we establish three operations on the set of axis-quasi-graduations of a module on which we also define an order relation. Finally, we compare the J-analytic spread of two axis-quasi-graduations of a module.

Received: July 18, 2025
Revised: September 15, 2025
Accepted: September 25, 2025

References

[1] D. G. Northcott and D. Rees, Reduction of ideals on local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145-158.

[2] Eugène D. Béché, Youssouf M. Diagana and Pierre K. Brou, Independence on quasi-bigraduation of rings and analytic spread, Afr. Math. Ann. AFMA 7 (2018), 129-136.

[3] G. Valla, Elementi independenti rispetto ad un ideale, Rend. Sem. Math. Univ. Padova 44 (1970), 339-354.

[4] G. Valla, Remarks on generalized analytic independence, Proc. Cambridge Philos. Soc. 85 (1974), 281-289.

[5] Y. M. Diagana, H. Dichi and D. Sangaré, Filtrations, generalized analytic independence, analytic spread, Afr. Mat. (3) 4 (1994), 101-114.

[6] Y. M. Diagana, Quasi-graduations of rings, generalized analytic independence, extensions of the analytic spread, Afr. Mat. (3) 15 (2003), 93-108.

[7] Y. M. Diagana, Quasi-graduations of rings and modules, criteria of generalized analytic independence, Afr. Math. Ann. AFMA 3 (2012), 65-78.

[8] Y. M. Diagana, Regular analytic independence and extensions of analytic spread, Comm. Algebra 30(6) (2002), 2745-2761.

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Published

2025-10-08

Issue

Vol. 64 No. 6 (2025)

Section

Articles

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How to Cite

CRITERIA OF $J$-INDEPENDENCE AND COMPARISON OF THE ANALYTIC SPREAD OF TWO $g$-AXIS-QUASI-GRADUATIONS OF AN $\mathcal{R}$-MODULE $\mathbb{M}$. (2025). JP Journal of Algebra, Number Theory and Applications, 64(6), 697-717. https://doi.org/10.17654/0972555525037

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