Regularity of Tensor Products Of $k$-Algebras
Copyright policy )Regularity of Tensor Products Of $k$-Algebras
This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field $k$. The main result establishes necessary and sufficient conditions for a Noetherian tensor product of two extension fields of $k$ to inherit regularity in various settings of separability. Thereby, we provide some applications as well as several original examples to illustrate or delimit the scope of the established results.
Mathematics - Algebraic Geometry, 13H05, 13H10, 13F15, 14M05, 16E65, FOS: Mathematics, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, 13H05, 13H10, 13F15, 14M05, 16E65, FOS: Mathematics, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Algebraic Geometry (math.AG)
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