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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Suppose we are given a pseudo-linearly convex triangle F . In [30], the main result was the construction of totally universal triangles. We show that S (π, ι̃) ∼ { 1 ‖Ī‖ : √ 2 −4 = ⋂ X ( R′ )}
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Some of the so called smallness conditions in algebra as well as in category theory, are important and interesting for their own and also tightly related to injectivity, are essential boundedness, cogenerating set, and residual smallness. In this overview paper, we first try to refresh these smallness condition by giving the detailed proofs of the results mainly by Bernhard Banaschewski and W...
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Characterizations of quasi-continuousmodules and continuousmodules are given. A non-trivial generalization of injectivity (distinct from p-injectivity) is considered.
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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...
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2009
ISSN: 1225-6951
DOI: 10.5666/kmj.2009.49.2.389