Authors define very nice and modest algebras axiomatically to link Hilbert-Samuel polynomials with multiplicity, generalize prior results from Ore domains to prime algebras, and establish the property for rational Cherednik algebras.
Gr\" o bner bases
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Presents a lifting technique to compute strong Gröbner bases over R/nR by reducing computations over R/nR to those over R/aR and R/bR for coprime a and b, recursing to fields for squarefree n via non-invertible coefficient detection.
citing papers explorer
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Hilbert-Samuel Polynomials for Algebras with Special Filtrations
Authors define very nice and modest algebras axiomatically to link Hilbert-Samuel polynomials with multiplicity, generalize prior results from Ore domains to prime algebras, and establish the property for rational Cherednik algebras.
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Efficient Gr\"obner Bases Computation over Principal Ideal Rings
Presents a lifting technique to compute strong Gröbner bases over R/nR by reducing computations over R/nR to those over R/aR and R/bR for coprime a and b, recursing to fields for squarefree n via non-invertible coefficient detection.