Let $R$ be a unital *-ring. Assume that $R$ has finitely many projections.
Q. Can we conclude that $R$ is finite?!
$\bullet$ We say $R$ is finite if $x^*x=1_R$ implies that $xx^*=1_R$.
$\bullet$ $p\in R$ is called a projection if $p=p^*=p^2$.
Let $R$ be a unital *-ring. Assume that $R$ has finitely many projections.
Q. Can we conclude that $R$ is finite?!
$\bullet$ We say $R$ is finite if $x^*x=1_R$ implies that $xx^*=1_R$.
$\bullet$ $p\in R$ is called a projection if $p=p^*=p^2$.