… In complete analogy with the finite topology, we define a natural linear topology on the ring
S $\mathfrak {S}$ , which we call the compact topology. The base of open left ideals of S $\…

… ) be a recollement of module categories for artin algebras Λ … mod Λ is tilting when the given
two torsion pairs are tilting in mod … of tilting modules in mod Λ with respect to tilting modules in …

… [26] which focused on (co)tilting modules of homological dimensions at most one) is the …
Gabriel topology. We refer to [41, Section VI.5] for the general definition of a Gabriel topology…

… They play an important role in topological quantum field theories in dimension 2 and even
3 (see [8]) and in representation theory and knot theory (see [9–11]). Also, each Frobenius …

… }}$| is the abelian category of contramodules over a topological ring and that the derived
equivalences are realized by … Applying again the condition (ii) and Lemma 2.1, we conclude that …

… topology G associated to the 1-tilting class T over a commutative ring as illustrated by Hrbek.
We prove that a 1-tilting … (ii) Consider the following commuting triangle where N is G -torsion-…

… of nontopological modules with some completeness properties over a topological ring. More
… iso and for any family of groups Ci with s-power iso there is a natural s-power iso on II; Ci.) …

… –Reiten theory has connections to higher-dimensional geometry and topology [11], [12], [25],
[… 2.3 and statement (i) trivially implies (ii). It remains to show (ii) implies (i); we prove by con…

… tilting module T 0, one can always find a good tilting module T such that T and T 0 generate
the same full subcategory of the category A-Mod of all left A-modules… good tilting A-module T …

… tilting modules, especially from a monoidal perspective, which has been driven by work from
quantum topology … underpins the behavior of these tilting modules, known as the Temperley…