The endofinite spectrum of a tame algebra

Let R be a ring. Based on indecomposable endofinite R-modules and characters that were introduced by Crawley-Boevey [Modules of finite length over their endomorphism ring, in: S. Brenner, H. Tachikawa (Eds.), Representations of Algebras and Related Topics, in: London Math. Soc. Lecture Note Ser., vol. 168, 1992, pp. 127–184], we define the endofinite spectrum of the ring R. We compute this spectrum in some examples and study the behaviour of it under certain functors, with the objective of understanding the endofinite spectrum of tame algebras. Furthermore, we show that the endomorphism ring of a minimal point of the endofinite spectrum is a skew field. Hence the minimal points belong to the Cohn spectrum, as studied by Ringel [The spectrum of a finite dimensional algebra, in: Proc. Conf. on Ring Theory, Dekker, New York, 1979, pp. 535–598], which in turn is a subset of the endofinite spectrum. Finally, we introduce the normalised endofinite spectrum.