Corrigendum: Jacobi–Zariski long nearly exact sequences for associative algebras: (Bull. Lond. Math. Soc. 0 (2021) 1–15).

Assume that HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0011" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mo>/</mo><mi>B</mi></mrow></math> ht is a bounded HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0012" xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> ht -bimodule, with index of nilpotency HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0013" xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> ht and projective dimension HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0014" xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> ht . The Theorem and its proof read as follows: 6.5 Theorem Let HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0007" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>B</mi><mo> </mo><mi>A</mi></mrow></math> ht be an extension of HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0008" xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math> ht -algebras and let HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0009" xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> ht be an HT <math display="inline" altimg="urn:x-wiley:00246093:media:blms12549:blms12549-math-0010" xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> ht -bimodule. [Extracted from the article]