Sur Le Produit Tensoriel D’algèbres - Tabaâ, Mohamed (MATHEMATICA SCANDINAVICA, 2016)
Let σ A→ B and ρ A→ C be two homomorphisms of noetherian rings such that B_AC is a noetherian ring. We show that if σ is a regular (resp. complete intersection, resp. Gorenstein, resp. Cohen-Macaulay, resp. (S_n), resp. almost Cohen-Macaulay) homomorphism, so is σI_C and the converse is true if ρ is faithfully flat. We deduce the transfer of the previous properties of B and C to B_AC, and then to the completed tensor product B_AC. If B_AB is noetherian and σ is flat, we give a necessary and sufficient condition for B_AB to be a regular ring.