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GENERALIZED SAMUEL NUMBER $wbar_phi(theta)$ AND AXE-FILTRATIONS ON A SEMIMODULE
Keywords:
semiring, regular quasi-filtration, AP quasi-filtration, generalized Samuel numbersDOI:
https://doi.org/10.17654/0972555526003Abstract
This work extends the theory of Samuel numbers to semimodules by introducing a generalized number, $wbar_phi(theta)$ for two axe-filtrations. We establish its existence under regularity conditions, including the Approximable by Powers (AP) and weakly good properties. By adapting the concept of valuative reduction, we prove that this invariant is well-defined and robust, laying the foundation for a quantitative analysis of filtration structures on semimodules.
Received: September 19, 2025
Accepted: November 1, 2025
References
References
[1] K. P. Brou and E. D. Béché, Deep classification of a generalization of ring filtration in commutative algebra, International Journal of Algebra 19(2) (2025), 79-88. https://doi.org/10.12988/ija.2025.91962
[2] E. D. Akeke, S. Ouattara and P. Ayegnon, Another generalized Samuel number on a semi-ring, JP J. Algebra Number Theory Appl. 36(2) (2015), 123-139.
[3] E. D. Akeke and P. Ayegnon, Some aspects of generalized Samuel numbers and quasi graduations on a semi-ring, Pioneer J. Algebra Number Theory Appl. 5(1) (2013), 17-28.
[4] S. Ouattara, E. D. Akeke and P. Ayégnon, Generalized Samuel numbers and on a semi-module, Afr. Math. Ann. (AFMA) 2 (2011), 175-189.
[5] S. Ouattara, E. D. Akeke and P. Ayegnon, Another generalized Samuel number on a semi-ring, JP J. Algebra Number Theory Appl. 19(2) (2010), 185-201.
[6] M. Lejeune-Jalabert and B. Teissier, Integral closure of ideals and equisingularity, Ann. Fac. Sci. Toulouse Math. 17 (2008), 781-859.
[7] P. Ayégnon, Filtrations on a set and Samuel numbers, Afr. Mat. Ser. III 16 (2005), 139-144.
[8] P. Ayegnon, Extensions to filtrations of Samuel numbers associated with ideals, Communication in Algebra 22(9) (1994), 3249-3263.
[9] J. W. Petro, Some Results in the Theory of Pseudo-valuations, Ph.D. Dissertation, State University of Iowa, Iowa City, 1961.
[10] D. Rees, Variations associated with a local ring (1), Proc. London Math. Soc. (Series 3) 5 (1955), 107-128.
[11] P. Samuel, Some asymptotic properties of powers of ideals, Ann. of Math. 56 (1952), 11-21.
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