# Ring detail

## Name: Non-symmetric $2$-primal ring

Description: Consider the semigroup $S=\{a,b\}$ with $a^2=ab=a$,$b^2=ba=b$. Make the semigroup ring $T=F_2[S]$. Make the Dorroh extension $T'=\mathbb Z(+)T$. $T'$ is the ring.

Krull dimension: (unknown)

Keywords Dorroh extension

Reference(s):

• G. Marks. Reversible and symmetric rings. (2002) @ Example 2, p 313