I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ...(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Simple Unitial Rings .... centre is a field ... ? ...

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**