Warfield domains: module theory from linear algebra to commutative algebra through abelian groups
In this well-written survey, the author has three main goals. The first goal is to outline the chronological development of the theory of reflexive and related domains from the sixties to the present days. The second goal is to illustrate the various characterizations of Warfield domains: the non-intrinsic ones through the reflexivity of their overrings, and the intrinsic ones in the classical cases of Noetherian and integrally closed domains, and in the general case. The third goal is to present a series of results on the good behaviour of the torsionless modules of finite rank over Warfield domains with respect to direct sum decompositions. This subject goes back to a pioneering theorem in Steinitz's 1912 paper [cf. \textit{E. Steinitz}, Math. Ann. 72, 297--345 (1912; JFM 43.0274.01)].
scientific article; zbMATH DE number 2099224