Left inverse of an algebra element
= Left inverse of an algebra element
{title2=$ba=1$}
A left inverse of an element $a$ of a unital <associative algebra> is an element $b$ with $ba=1$. A right inverse instead satisfies $ab=1$. If both exist, they agree: $b=b(ac)=(ba)c=c$. A one-sided inverse alone need not imply invertibility in an infinite-dimensional <Banach algebra>.