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Projective modules and Gröbner bases for skew PBW extensions. (English) Zbl 1371.16001

Summary: Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincaré-Birkhoff-Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.

MSC:

16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras
16Z05 Computational aspects of associative rings (general theory)
16D40 Free, projective, and flat modules and ideals in associative algebras
16S38 Rings arising from noncommutative algebraic geometry

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References:

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