منابع مشابه
Some Comments on Injectivity and P-injectivity
A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End(AM), then E/J(E) is von Neumann regular, where J(E) is the Jacobson radical of the ring E. A is semisimple Artinian if, and only if, every left A-module is GI. If A is a left p. p., left GI-ring su...
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A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...
متن کاملEssentiality and Injectivity
Essentiality is an important notion closely related to injectivity. Depending on a class M of morphisms of a category A, three different types of essentiality are considered in literature. Each has its own benefits in regards with the behaviour of M-injectivity. In this paper we intend to study these different notions of essentiality and to investigate their relations to injectivity and among t...
متن کاملInjectivity and adjoint extremals
The following investigation deals with injectivity results for general diffeomorphisms as well as for Haar’s transformation. We apply these results to adjoint variational problems introduced by Haar [6]. In particular, we prove a generalization of Krust’s theorem for two-dimensional adjoint extremals. AMS Classification Code: 26B10, 49B, 49L, 53A05, 53A10, 70G, 70H
متن کاملApproximate Injectivity
In a locally λ-presentable category, with λ a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are λ-presentable, are known to be characterized by their closure under products, λ-directed colimits and λ-pure subobjects. Replacing the strict commutativity of diagrams by “commutativity up to ε”, this paper provides an “appro...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2020
ISSN: 0166-8641
DOI: 10.1016/j.topol.2020.107503