Forcing linearity numbers for modules over rings with nontrivial idempotents (Q1858208)

Let \(R\) be a ring and \(V\) an \(R\) module. All rings in this paper are associative, have an identity 1, and all modules are unital. The authors determine forcing linearity numbers of \(V\) in terms of certain modules over the rings \(e_iRe_i\). If each \(e_iRe_i\) is a division ring they obtain precise answers. They find the forcing linearity numbers for all modules over Artinian rings. The paper is divided into the sections of Introduction; General Results; Determination of Forcing Linear Numbers; Applications and Remarks; and Forcing Linearity Numbers over Artinian Rings. In the last section, instead of focusing on properties of the decomposition of the modules \(e_iV\), they focus on properties of the rings \(e_iRe_i\).