… Gabriel topologies and their bijective correspondence with hereditary torsion pairs. Furthermore
we will define rings and modules of quotients with respect to a Gabriel … submodules …

… We prove that if M is a finitely generated R-module, progenerator in σ[M] and χ ̸= τ is FIS-…
[9, Proposition 1.12] we have that every prime submodule P of M contains a minimal prime …

… M has enough noetherians if any nonzero submodule of M … only if M has Gabriel dimension
and for every p ∈ Supp ( M ) … a module M which has enough noetherians but M is not locally …

… Let p be a prime number and K a local field of residue … hypothetical local mod p
correspondence for GL2(K) by purely local (… a finite set of bad places Σ in the definition of m, but …

… of Gabriel's correspondence, which originally related indecomposable injective modules and
prime … with the set of prime ideals, and for a locally noetherian Grothendieck category, the …

… by the Deligne–Grothendieck–Serre correspondence [8, 20.3.16 (iv… a finite number of F-stable
submodules; in particular, we … sums we deduce from the Matlis–Gabriel theorem [8, 10.1.9] …

… correspondence between the simple objects and the indecomposable injectives for this
category (resulting in a description of the Gabriel … Then any simple FΨJ 〈SΨ|J 〉-submodule M …

… In the fourth section we will study the theory of the local and global theta correspondence,
showing why are both notions compatible and further, showing how to relate the singular theta …

… , we prove that if M is projective in the category σ[M], then Prt(… bijective correspondence
between maximal submodules of M … N is a prime submodule of M, then ann(M/N) is a prime ideal. …

… We say that M is locally free if there exist f1,...,fn ∈ A … It’s possible to restrict our correspondence
yet one more time to obtain … If N is a submodule of M such that M = N + IM, then M = N. …