# Units in matrix rings over non commutative ring with unity

1)This book "introduction to Rings and Modules" by C. Mussili, says determinant of a matrix over non commutative ring is not defined. But in defining the determinant of a matrix where the commutativity of the ring is used.

2) Please suggest some texts to study group of units of matrix rings over non commutative rings.

• The definition does not use commutativity, but most properties do. – darij grinberg Jun 1 at 5:54
• Not "the determinant over noncommutative ring is not defined" but rather "the usual definition is not suitable" There are certainly definitions of determinants used with noncommutative fields. – rschwieb Jun 3 at 13:09

In particular Chapter 9 is about matrix algebras $$M_n(D)$$ over a division algebra $$D$$.