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O que (quem) é injective resolution - definição
MODULE SUCH THAT INFINITE SYSTEMS OF LINEAR EQUATIONS CAN BE SOLVED BY SOLVING FINITE SUBSYSTEMS
Algebraically compact; Pure injective module; Pure-injective; Pure-injective module
Resolution (algebra)
IN ALGEBRA, AN EXACT SEQUENCE WHICH IS USED TO DESCRIBE THE STRUCTURE OF AN OBJECT
Injective resolution; Projective resolution; Free resolution; Flat resolution; Finite resolution; Minimal free resolution; Projective resolution and free resolution; Wikipedia talk:Articles for creation/Projective resolutions and free resolutions; Projective resolutions and free resolutions; Resolution of a module; Resolution (homological algebra); Acyclic resolution; Minimal resolution (algebra); Coresolution; Left resolution; Right resolution
In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution uses coresolution, though right resolution is more common, as in ) is an exact sequence of modules (or, more generally, of objects of an abelian category), which is used to define invariants characterizing the structure of a specific module or object of this category. When, as usually, arrows are oriented to the right, the sequence is supposed to be infinite to the left for (left) resolutions, and to the right for right resolutions.
Injective hull
NOTION IN ABSTRACT ALGEBRA
Module of finite rank; Injective envelope
In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it. Injective hulls were first described in .
Resolution (logic)
IN LOGIC, RULE OF INFERENCE
First-order resolution; First order resolution; Logical resolution; Binary resolution; Resolution principle; Robinson`s resolution principle; Method of resolution; Robinson's Resolution Algorithm; Resolvent (logic); Resolution inference; Resolution prover; Non-clausal resolution; Paramodulation
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem.
Wikipédia
Algebraically compact module
In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution of infinite systems of equations in the module by finitary means. The solutions to these systems allow the extension of certain kinds of module homomorphisms. These algebraically compact modules are analogous to injective modules, where one can extend all module homomorphisms. All injective modules are algebraically compact, and the analogy between the two is made quite precise by a category embedding.
