Filtered-graded transfer of noncommutative Gröbner bases

As the case of free k-algebras and PBW algebras, given a bijective skew PBW extension A, we will show that it is possible transfer Gröbner bases between A and its associated graded ring.

DOI: https://doi.org/10.15446/recolma.v50n1.62179

Transferencia filtrado-graduado de bases de Gröbner no conmutativas

Claudia Gallego¹

¹ Universidad Nacional de Colombia, Bogotá, Colombia cmgallegoj@unal.edu.co

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Abstract

Keywords: Noncommutative Gröbner bases; skew PBW extensions; filtered module; graded module.

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2010 Mathematics Subject Classification: Primary: 16Z05. Secondary: 16W70, 16W50.

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Resumen

Como en el caso de k-álgebras libres y PBW álgebras, dada A una extensión PBW torcida biyectiva, mostraremos que es posible transferir bases de Gröbner entre A y su anillo graduado asociado.

Palabras claves: Bases de Gröbner no conmutativas; extensiones PBW torcidas; módulo filtrado; módulo graduado.

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References

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(Recibido: enero de 2016 Aceptado: febrero de 2015)