Proposition 1.1. Let f : R1 → R2 be a homomorphism of rings. If J is an ideal of R2, then f (J) is an ideal of R1 containing ker(f) and furthermore f(f(J)) ⊆ J . Now let f : R1 → R2 be an epimorphism of rings. If J is an ideal of R2 then f(f (J)) = J . If I is an ideal of R1 then f(I) is an ideal of R2. Furthermore we have I ⊆ f (f(I)) = I + ker(f) and thus I = f(f(I)) if I contains ker(f). Thu...

Angell’s logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC Ferguson, and 16-valued Fine. It is that the former image surjective homomorphism from latter, i.e., an epimorphic image. Some candidate 7-valued matrices are ruled out as characteristic AC. Whether with fewer than 9 values exist remains open question. The results were obtained help MUltlog syst...

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is universal localization. As an application, prove the Telescope Conjecture holds for unbounded derived categories of rings commutative).

Given an epimorphism φ: Π → Π' between projective planes Π and Π', it is an open question how the groups of projectivities of Π and Π' (regarded as permutation groups on projective lines) are related. Within this note we will not answer this sophisticated and hard problem in full, but we will address the question to which extend the projectivities of Π induce permutations on the lines of Π ' wh...

Given a nitely presented group G and an epimorphism : G ! Z, constraints on the orders of automorphisms F : G ! G such that F = are obtained via symbolic dynamics. The techniques provide new obstructions to periodicity for knots and links.

We prove that the separating space of an epimorphism from a Lie–Banach algebra onto the (continuous) derivation algebra Der(A) of a Banach algebra A consists of derivations which map into the radical of A.

We show that the category of regular epimorphisms in a Barr exact Goursat category is almost Barr exact in the sense that (it is a regular category and) every regular epimorphism in it is an effective descent morphism.

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.

We are concerned with the following problem. Suppose ? and are closed permutation groups on innnite sets C and W and : ? ?! is a non-split, continuous epimorphism with nite kernel. Describe (for xed) the possibilities for. Here, we consider the case where arises from a nite cover : C ?! W. We give reasonably general conditions on the permutation structure hW; i which allow us to prove that thes...