Brandt semigroup

In mathematics, Brandt semigroups are completely 0-simple inverse semigroups. In other words, they are semigroups without proper ideals and which are also inverse semigroups. They are built in the same way as completely 0-simple semigroups:

Let G be a group and ${\displaystyle I,J}$ be non-empty sets. Define a matrix ${\displaystyle P}$ of dimension ${\displaystyle |I|\times |J|}$ with entries in ${\displaystyle G^{0}=G\cup \{0\}.}$

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