# 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.

Notes:

Keywords Dorroh extension

Reference(s):

• Greg Marks, Reversible And Symmetric Rings, Journal Of Pure And Applied Algebra Volume 174, Issue 3, Pp 311–318, (2002). Example 2 P 313

This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: