MATH145 Lecture Notes - Lecture 20: Zero Divisor, Additive Inverse

• School: University of Waterloo
• Department: Mathematics
• Course: MATH145
• Professor: Stephen New

Document Summary

X y z (x + y ) + z = x + (y + z ) X y x + y = y + x. X y z (x y )z = x (y z ) X y z x (y + z ) = x y + x z (x + y )z = x z + y z. X ( x = 0 y (x y = 1 y x = 1)) Let a, b r. if ab = 1 we sat that a is a left inverse of b and b is a right inverse of a. If ab = ba = 1, then we say that a and b are (2-sided) inverses of each other. We say that a r is invertible or that a is a unit when a has a (2-sided) inverse b. If a 6= 0 and b 6= 0 and ab = 0 then a and b are called zero divisors.