1. Introduction. The purpose of this essay “is to highlight the connec-tions and interplay
between the concepts of epimorphisms, dominions and amalgams. This will be done largely …

The space of homomorphisms between a projective object and a Verma module in category
𝓞 inherits an induced filtration from the Jantzen filtration on the Verma module. On the other …

We introduce a symmetry property for unit-regular rings as follows: a∈ R is unit-regular if
and only if aR⊕(a− u) R= R (equivalently, Ra⊕ R (a− u)= R) for some unit u of R if and only …

Finally, let B and 8 be two rings, let 9 be a full subcategory of left R-modules closed under
direct sums and factor modules, let be a full subcategory of left S-modules containing ss and …

If R is regular local and M, N are finitely generated modules over R, then by S.
Lichtenbaum's theorem [5], the vanishing of Tor~(M, N) for some i> 1, implies that of Torf (M …

In this article we first give the relations between commonly used images of a morphism in a
category. We then investigate d-homology in a category with certain properties, for a kernel …

All rings that we consider in this paper are assumed to be commutative and noetherian. R
and A will always denote a ring of this kind. The modules that we consider are also assumed …

Endomorphism rings of projective modules Page 1 Math. Z. 111, 322-332 (1969)
Endomorphism Rings of Projective Modules* FRANK W. ANDERSON Introduction Let R and S …

A well-known theorem of Kaplansky states that any projective module is a direct sum of
countably generated modules. In this paper, we prove the w-version of this theorem, where …

In this section we collect some basic properties of stable equivalences. Using generic
modules, we prove at the end that a stable equivalence preserves strongly unbounded …