Let $K$ be a finite field and $G$ be a discrete group. 



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> Is it true that for every $a=e+a\_1+\ldots+a\_n,b=e+b\_1+\ldots+b\_m\in K[G]$ with $b\_i\neq e,a\_j\neq e$ the condition $ab=0$ implies $ba=0$?
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It is related to [this](https://mathoverflow.net/questions/58267/group-ring-and-left-zero-divisor) question. 
The examples proposed there do not violate the condition above.



Group ring and left zero divisor II
I hope I understand the question right: the $a\_i$ are to be distinct elements of $G$, as are the $b\_j$?


If so, then the answer is no. Let $K$ be $\mathbb Z/2$ and suppose that $x$ and $y$ are elements of $G$ such that $x^2=e$ and $xy$ is not equal to $yx$. Let $a=e+x$ and let $b=(e+x)(e+y)=e+x+y+xy$. Then $ab=0$ but $ba=y+xy+yx+xyx$ is not $0$.


