 #1
Math Amateur
Gold Member
 1,067
 47
I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ...
I need help with some remarks of Bresar in Example 1.21 on simple unital rings ...
Example 1.21 reads as follows:
In the above text from Bresar, we read the following:
" ... ... Indeed, if ##c## is a nonzero central element, then ##cA## must be, as a nonzero idea of ##A##, equal to ##A##. This implies that ##c## is invertible. ... ... "
Can someone please show me exactly why it is the case that ##cA## being equal to ##A## implies that ##c## is invertible ...
Help will be appreciated ...
Peter
I need help with some remarks of Bresar in Example 1.21 on simple unital rings ...
Example 1.21 reads as follows:
In the above text from Bresar, we read the following:
" ... ... Indeed, if ##c## is a nonzero central element, then ##cA## must be, as a nonzero idea of ##A##, equal to ##A##. This implies that ##c## is invertible. ... ... "
Can someone please show me exactly why it is the case that ##cA## being equal to ##A## implies that ##c## is invertible ...
Help will be appreciated ...
Peter
Attachments

64.9 KB Views: 561