gr(D_n) and gr(ε_p) Are Not Noetherian Rings With Pure Dimension

doi:https://doi.org/10.1360/sb1993-38-13-1060

Article10.1360/sb1993-38-13-1060

gr(D_n) and gr(ε_p) Are Not Noetherian Rings With Pure Dimension

吴泉水-1993-07-15-Acta Scientiarum Naturalium Universitatis Sunyatseni

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TL;DRAbstract

A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that if R is a finitely generated commutative algebra over some field, R is integral and gl. dimR<∞, then R is a regular Noetherian ring with pure dimension. Let D(V) be the ring of differential operators over the non-singular n-dimensional irreducible algebraic variety V. Then gr(D(V)) is a regular

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A commutative Noetherian ring R is called a regular Noetherian ring with pure dimension n, if for any maximal ideal m of R, gl.dimR_m=n, where R_m is the localization of R at the maximal ideal m. It is well known that if R is a finitely generated commutative algebra over some field, R is integral and gl. dimR<∞, then R is a regular Noetherian ring with pure dimension. Let D(V) be the ring of differential operators over the non-singular n-dimensional irreducible algebraic variety V. Then gr(D(V)) is a regular

Keywords

MathematicsNoetherianNoetherian ringLocal ringGlobal dimensionIdeal (ethics)Pure mathematicsDimension (graph theory)

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