Downloads provided by UsageCountsNoetherian rings of low global dimension and syzygetic prime ideals
Copyright policy ) Planas Vilanova, Francesc d'Assís;
Noetherian rings of low global dimension and syzygetic prime ideals
Let $R$ be a Noetherian ring. We prove that $R$ has global dimension at most two if, and only if, every prime ideal of $R$ is of linear type. Similarly, we show that $R$ has global dimension at most three if, and only if, every prime ideal of $R$ is syzygetic. As a consequence, one derives a characterization of these rings using the André-Quillen homology.
Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::13 Commutative rings and algebras::13H Local rings and semilocal rings, Homological dimension and commutative rings, syzygetic ideal, Multiplicity theory and related topics, Noetherian regular rings, global dimension, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Classificació AMS::13 Commutative rings and algebras::13D Homological methods, 13A30, 13D05, 13D03, 13H05, 13H15, Global dimension, Syzygetic ideal, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, FOS: Mathematics, ideal of linear type, Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory, Regular local rings, Ideal of linear type
Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::13 Commutative rings and algebras::13H Local rings and semilocal rings, Homological dimension and commutative rings, syzygetic ideal, Multiplicity theory and related topics, Noetherian regular rings, global dimension, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Classificació AMS::13 Commutative rings and algebras::13D Homological methods, 13A30, 13D05, 13D03, 13H05, 13H15, Global dimension, Syzygetic ideal, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, FOS: Mathematics, ideal of linear type, Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory, Regular local rings, Ideal of linear type
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