Hall's identity explained

In mathematics, Hall's identity may be:

[x, y ^{-1} , z] ^{y ⋅ [y,} z ^{-1} , x] ^{z ⋅ [z,} x ^{-1} , y] ^{x} = 1

• The Hall identity [[''x'',''y'']²,z] = 0 for 2 by 2 matrices, showing that this is a polynomial identity ring
• The Hall–Petresco identity for groups expressing x^my^m in terms of powers of elements of the descending central series.