Locally polynomial algebras are symmetric

H. Bass, E. H. Connell, D. L. Wright
1976 Bulletin of the American Mathematical Society  
is proved by reducing it to part (a). Part (a) is proved by first constructing an augmentation A -> K and then applying the following general result, which has various other applications. THEOREM 4. Let A be a finitely presented {not necessarily commutative) K-algebra equipped with an augmentation, 0 -> A -> A -> K -> 0, and put 7A = (B n>0 A n /A n + 1 , the associated graded algebra. If A n = yA m (as filtered algebras) for all m G max(AT), then A = y A.
doi:10.1090/s0002-9904-1976-14128-6 fatcat:xe6lwvi7kvf3llfs3qlkn5ulya