All $n$-cotilting modules are pure-injective
نویسندگان
چکیده
منابع مشابه
Pure-injective modules
The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...
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Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations. We describe the relation in terms of pointed modules. We present methods for producing superdecomposable pure-injectives and give some details of recent work of Harland doing this in the context of tubular algebras. 2010 Mathematics Subject Classification. Primary 16G...
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We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are “tame” according to the Klingler–Levy analysis in [4], [5] and [6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.
متن کاملPure-injective hulls of modules over valuation rings
If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...
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We give a criterion for the existence of a super-decomposable pure-injective module over an arbitrary serial ring.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-06-08256-6