… the existence of D-envelopes (respectively, D-covers) and the existence of Hom(C, D)-envelopes
or C ⊗D-envelopes (respectively, Hom(C, D)covers or C ⊗ D-covers) of modules. As a …

… of classical notions, such as injective envelopes or projective covers, and on the other
hand, it … We consider an arbitrary ring R and discuss the existence of precovers and preenvelopes …

… In Section 5, we discuss the existence of -(pre)covers of complexes which is based on an
idea due to Iacob [Citation19]. Let ℱ be a class of R-modules closed under extensions, then we …

… dimension 1 covers and divisible envelopes we will assume … the kernels of covers and the
cokernels of envelopes belong to … For the existence of divisible envelopes we have succeeded …

… Envelopes and covers provide common frames for a number of classical notions such as
injective envelopes and projective covers, and turn out to be extremely fruitful for general …

… Dually, we have the definitions of a -precover and a -cover (with the unique mapping
property). -envelopes (-covers) may not exist in general, but if they exist, they are unique up …

… covers exist in the category of topological spaces. Algebraic closures of elds are envelopes
in … The notion of a total integral closure of a commutative ring R is an envelope which extends …

… Further, if the class of all X-projective R-modules is closed under direct limits, we show
the existence of X⊥-projective covers and X-injective envelopes over a X⊥hereditary ring R. …

… A detailed introduction that covers everything we need is given in [Neu19, Chapter 2]. …
exists an envelope F : X → L of f : X → Y such that for all effective injective spaces M there exists …

… We note thatAuslander and Reiten consider similar questions in [2] but concerning finitely …
prove the existence of covers (envelopes) once precover (preenvelopes) are known to exist. In …