Geodesic
On modular computation of Gröbner bases with integer coefficients
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 133-137 
S. Yu. Orevkov. On modular computation of Gröbner bases with integer coefficients. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 133-137. http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a10/
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     author = {S. Yu. Orevkov},
     title = {On modular computation of {Gr\"obner} bases with integer coefficients},
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     pages = {133--137},
     year = {2014},
     volume = {421},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\mathbb Z[X]$, $X=(x_1,\dots,x_n)$ and let $I$ be their union. We propose an algorithm to compute the Gröbner base of $I$ under the assumption that the Gröbner bases of the ideal $\mathbb QI$ of the ring $\mathbb Q[X]$ and the the ideals $I\otimes(\mathbb Z/m\mathbb Z)$ of the rings $(\mathbb Z/m\mathbb Z)[X]$ are known. Such an algorithmic problem arises, for example, in the construction of Markov and semi-Markov traces on cubic Hecke algebras.

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[6] S. Yu. Orevkov, “Kubicheskie algebry Gekke i invarianty transversalnykh zatseplenii”, DAN (to appear)