On sets of subspaces closed under reguli (Q1185851)

Let \(F\) be a field with \(| F| > 2\) and \(A\) an \(F\)-algebra, associative with 1, where \(A^*\) denotes the group of unities of \(A\). For \(a\in A\) let \(e(a)=\{f\in F\mid a-f\in A^*\}\). The \(F\)-algebra \(A\) is called strong iff \(| e(a)| > | F\setminus e(a)|\). The author gives an algebraic description of the weak subspaces of the chain geometry \(\sum_ F(U,A)\) where \(U\) is a cyclic and faithful right- \(A\)-module and \(A\) is a strong \(F\)-algebra. He also considers the special case \(A=End_ FU\) for an \(F\)-vector space \(U\) of dimension \(r<\infty\) and \(| F| > 2r\).