Notation and Background; Regular Homomorphisms; Indecomposable Modules; Regularity in Modules; Regularity in HomR(A, M) as a One-sided Module; Relative Regularity: U -Regularity and Semiregularity; Reg(A, M) and Other Substructures of Hom; Regularity in Homomorphism Groups of Abelian Groups; Regularity in Categories
Summary
Generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. This work characterizes regular homomorphisms in terms of decompositions of domain and codomain, and presents numerous other results
