The goal of this work is to develop a functional transfer of properties between a module A
and the category* M* E of right modules over its endomorphism ring* E that is more sensitive …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

By a well known theorem of K. Morita, any equivalence between full module categories over
rings R and S, are given by a bimodule RPS, such that RP is a finitely generated projective …

Conditions for the endomorphism ring of a (finitely generated) projective module to be left
(semi) hereditary have been studied in several papers ([2],[7],[8]). In [2] and [8] it is shown …

Self-injective and PF endomorphism rings Page 1 ISRAEL JOURNAL OF MATHEMATICS, Vol.
58, No. 3, 1987 SELF-INJECTIVE AND PF ENDOMORPHISM RINGS BY JL GARCiA …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

We show that categories of modules over a ring in homotopy type theory (HoTT) satisfy the
internal versions of the AB axioms from homological algebra. The main subtlety lies in …

This paper is based upon joint work with Maurice Auslander. It is closely related to his
lecture in the workshop at ICRA VII, and a special effort has been made to emphasize the …