an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

Cryptosystems based on supersingular isogenies have been proposed recently for use in post-quantum cryptography. Three problems have emerged related to their hardness: computing an isogeny between two curves, computing the endomorphism ring of a curve, and computing a maximal order associated to it. While some of these problems are believed to be polynomial-time equivalent based on heuristics, ...

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

Abstract We consider the dominant dimension of an order over a Cohen-Macaulay ring in category centrally modules. There is canonical tilting module case positive and we give upper bound on global its endomorphism ring.

It is well-known that modules with pathological properties can be obtained by constructing modules with \nearly prescribed" endomorphism rings. (See, for example, [5], [2], [3], or [10].) Here we shall investigate that method using a rather weak notion of nearly prescribing the endomorphism ring, namely one that just requires that a certain ring be algebraically closed in the endomorphism ring ...

We prove that any stable, additive, combinatorial model category M has a canonical model enrichment over Sp(sAb) (symmetric spectra based on simplicial abelian groups). So to any object X ∈ M one can attach an endomorphism ring object in this category, denoted hEndad(X). Since the homotopy theory of ring objects in Sp(sAb) is equivalent to the homotopy theory of differential graded algebras, on...

Let f be a continuous ring endomorphism of ZpJxK/Zp of degree p. We prove that if f acts on the tangent space at 0 by a uniformizer and commutes with an automorphism of infinite order, then it is necessarily an endomorphism of a formal group over Zp. The proof relies on finding a stable embedding of ZpJxK in Fontaine’s crystalline period ring with the property that f appears in the monoid of en...

A reformulation of Walker’s theorem on the cancellation of Z says that any two homomorphisms from an abelian group B onto Z have isomorphic kernels. It does not have a constructive proof, even for B a subgroup of Z3. In this paper we give a constructive proof of Walker’s theorem for B a direct sum, over any discrete index set, of groups of the following two kinds: finite-rank torsion-free group...