Generalized Koszul Properties of Commutative Local Rings
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Abstract
We study several properties of commutative local rings that generalize the notion of Koszul algebra. The properties are expressed in terms of the Ext algebra of the ring, or in terms of homological properties of powers of the maximal ideal of the ring. We analyze relationships between these properties and we identify large classes of rings that satisfy them. In particular, we prove that the Ext algebra of a compressed Gorenstein local ring of even socle degree is generated in degrees 1 and 2.
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Introduction -- Generalized Koszul rings -- Compressed Gorenstein local rings -- Conclusions and further questions
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Ph.D.