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Quasi-graduations of modules and extensions of analytic spread

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Let R be a ring and A a subring of R. Let \(h=\left( \mathcal {M} _{n}\right) _{n\in \mathbb {Z}\cup \left\{ +\infty \right\} }\) be a family of subgroups of an R-module \(\mathcal {M}\). We say that h is an A-quasi-graduation of \(\mathcal {M}\) if for every \(p\in \mathbb {N}, \mathcal {M}_{p}\) is a sub-A-module of R with \(\mathcal {M}_{\infty }=(0)\). We present weak notions of J-independence for different extensions of the analytic spread. We show that under some conditions they coincide with \(\lim \nolimits _{n \rightarrow +\infty }\ell _{J}(h^{(n!)},A,k)\), where, for all integers \(p, h^{(p)} = (\mathcal {M}_{pn})_{n\in \mathbb {Z}\cup \left\{ +\infty \right\} }\) and where \(\ell _J (h^{(p)}, A, k)\) is the maximum number of elements of J which are J-independent of order k with respect to the A-quasi-graduation \(h^{(p)}\) of the R-module \(\mathcal {M}\).

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Correspondence to Youssouf M. Diagana.

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Brou, P.K., Diagana, Y.M. Quasi-graduations of modules and extensions of analytic spread. Afr. Mat. 28, 1313–1325 (2017). https://doi.org/10.1007/s13370-017-0517-5

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  • DOI: https://doi.org/10.1007/s13370-017-0517-5

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