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math.RA2014
Hochschild Cohomological Dimension is Not Upper Semi-Continuous
Anastasis Kratsios
It is shown that the Hochschild Cohomological dimension of an associative algebra is not an upper-semi continuous function, showing the semi-continuity theorem is no longer valid f…
math.RA2014
Noncommutative Algebra and Noncommutative Geometry
Anastasis Kratsios
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an…
math.RA2014
Adjoinable Homology
Anastasis Kratsios
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. Thes…