Regularity of tensor products of k-algebras

Details Regularity of tensor products of k-algebras Regularity of tensor products of k-algebras

2012-02-25

arxiv.org/abs/1202.5615v1

Mathematics

Commutative Algebra

10 pages

Scientific paper

This paper tackles a problem on the possible transfer of regularity to tensor products of algebras over a field k. If K is a separable extension field of k and A is an arbitrary k-algebra, we prove that the tensor product of K and A is regular if and only if it is Noetherian and A is regular. As a consequence, we establish necessary and sufficient conditions for a Noetherian tensor product of two extension fields of k to inherit regularity in various settings of separability. Throughout, several original examples are provided to illustrate or delimit the scope of the established results.

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