An idea:

Assume $$\;a\in \bigcap_{M\le R\;max.}M\;$$

but nevertheless for some $\;b\in R\; $ we have that

$$1-ab\;\;\text{not a unit}\implies \text{the ideal}\;\langle 1-ab\rangle\;\;\text{is contained in some maximal ideal}\;\;M\le R$$

But $\;a\in M\implies 1\in M\iff M=R\;$ , and this cannot be.

Now suppose that for some maximal ideal $\;M\le R\;$ we have that $\;a\notin M\;$, so for maximality

$$\langle a\,,\,M\rangle =R\implies\;\exists \;b\in R\;,\;m\in M\;\;s.t.\;\; ab+m=1\implies$$

$$1-ab=m\in M\implies\;\;1-ab\;\;\text{cannot be a unit}$$

How to show $a$ is an element of every maximal ideal of ring $R$ iff $1-ab$ is a unit for all $b \in R$?
I am trying to do a very basic thing, which I though I should be able to manage all on my own, but alas.. 

What I am attempting to do, is to get hold of the values returned by "df -h", and to be able to store these values in a bash script array. The purpose is to combine it with other data (like the current timestamp) and output this to a new file/overwrite an existing file. 

The following two commands give me what I want on the commandline, but I cannot for the life of me load the output into an array that I can iterate over.

The followng gives me the disk utilization in percent for each disk: 

df -h | grep -vE "^Filesystem|shm|boot" |  awk '{ print +$5 }'


And the following gives me the disk path: 

df -h | grep -vE "^Filesystem|shm|boot" |  awk '{ print $6 }'


However, I am unable to assign the output of this into a variable inside a shell script that I can iterate over. 

ANY ideas and help would be very much appreciated!!
