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An R-algebra A is said to be a generalized E-algebra if A is isomorphic to the algebra EndR(A). Generalized E-algebras have been extensively investigated. In this work they are classified ‘modulo cotorsion-free modules’ when the underlying ring R is a Dedekind domain.
Goldsmith, B. & Gobel:Classifying, R. (2006). E-Algebras Over Dedekind Domains. Journal of Algebra, pg. 206, pg. 566-575. doi:10.1016/j.jalgebra.2006.01.036