Regular \(\mathcal J\)-classes of subspace semigroups
For a finite-dimensional algebra \(A\) over an infinite field \(K\), the subspace semigroup \({\mathcal S}(A)\) consists of all subspaces of \(A\) with operation \(V*W=\text{lin}_KVW\), the linear span of \(VW\) over \(K\). \({\mathcal S}(A)\) is strongly \(\pi\)-regular. It was first studied by the author and \textit{M. S. Putcha} [J. Algebra 233, No. 1, 87-104 (2000; Zbl 0983.20062)]. The author studies the completely \(0\)-simple principal factors of \({\mathcal S}(M_n(K))\). Idempotents and regular \(\mathcal J\)-classes are characterized and some symmetries of \({\mathcal S}(M_n(K))\) are established.
completely \(0\)-simple principal factors
scientific article; zbMATH DE number 1837344