  We characterize the intra-regular $\Gamma$-semigroups and the left regular
$\Gamma$-semigroups $M$ in which $x\Gamma M\subseteq M\Gamma x$ for every $x\in
M$ in terms of filters and we prove, among others, that every intra-regular
$\Gamma$-semigroup is decomposable into simple components, and every
$\Gamma$-semigroup $M$ for which $x\Gamma M\subseteq M\Gamma x$ is left
regular, is decomposable into left simple components.
