… (This is in purely formal analogy with Einjective, ie, ▲ is a formal symbol whose properties
we propose to elucidate.) As stated, the theorem of Teply and Miller implies that A-injective → …

… In this section we prove that a pure projective 1-tilting module over a commutative ring is …
The property gi+1fi+1fi = fi shows that ϕi+1fi = ϕi for every i ≥ 2. The universal property of direct …

… Furthermore, our argument allows us to directly deduce the identification of H Z as an E 2
-Thom ring spectrum. Finally, we describe the topological Hochschild homology and the E n -…

… when S is closed under finite intersection), we are invited to consider the direct limit ring lim
… Finally, we see as above that every ring of quotients of A is a ring of continuous functions on …

… In our study of modules over general rings the central … rings with this property are characterised
by the fact that every (cyclic) singular left /2-module is a direct sum of an injective module …

… This module-theoretic property has a remarkable consequence at the level of chain … But
then, by Theorem 5.1(2) (whose argument is still valid for a category of unital modules over a ring …

… In the study of modules over hereditary rings of finite representation type we need an alternative
description of the set V presented below. Assume that two integers 0 < s < oo and 0 < m …

… of persistence modules has a number of useful properties (… ring in what follows and we will
always assume that our rings … -modules over a unital ring R and R-module homomorphisms…

… The hope is that the graph-theoretic properties of the graph from the ring will help us better
… (We will often write 0 for {0} in a ring or module.) It is clear that M is a reduced module if and …

… To state our result let us denote by R ( G ) ‾ the representation ring of kG modulo projectives
and for any kG-module V let V ‾ be the element of R ( G ) ‾ corresponding to V. Finally, write …