Formally smooth bimodules
Copyright policy )Formally smooth bimodules
The notion of a formally smooth bimodule is introduced and its basic properties are analyzed. In particular it is proven that a $B$-$A$ bimodule $M$ which is a generator left $B$-module is formally smooth if and only if the $M$-Hochschild dimension of $B$ is at most one. It is also shown that modules $M$ which are generators in the category $��[M]$ of $M$-subgenerated modules provide natural examples of formally smooth bimodules.
17 pages
- University of Ferrara Italy
- University of Turin Italy
- Swansea University United Kingdom
Hochschild cohomology groups, Bimodules in associative algebras, Algebra and Number Theory, Noncommutative algebraic geometry, separable bimodules, Mathematics - Rings and Algebras, Relative homological algebra, projective classes (category-theoretic aspects), formally smooth bimodules, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Relative projectivity; cohomology; formally smooth module; separable module., FOS: Mathematics, 16D20, 14A22
Hochschild cohomology groups, Bimodules in associative algebras, Algebra and Number Theory, Noncommutative algebraic geometry, separable bimodules, Mathematics - Rings and Algebras, Relative homological algebra, projective classes (category-theoretic aspects), formally smooth bimodules, Rings and Algebras (math.RA), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Relative projectivity; cohomology; formally smooth module; separable module., FOS: Mathematics, 16D20, 14A22
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