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Injective Hulls of Modules [PDF]

, 1966
Doctor of Philosophy (PhD)
Tiwary, Awadhesh Kumar
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The Lipschitz injective hull of Lipschitz operator ideals and applications

Banach Journal of Mathematical Analysis, 2020
We introduce and study the Lipschitz injective hull of Lipschitz operator ideals defined between metric spaces. We show some properties and apply the results to the ideal of Lipschitz p-nuclear operators, obtaining the ideal of Lipschitz quasi p-nuclear ...
Elhadj Dahia, Daniel Carando, Dahmane Achour   +2 more
exaly   +2 more sources

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Injective Hulls are Completions of Ordered Algebras

Order, 2023
Let \(P\) be a poset. A subset \(S\subseteq P\) is called a \textit{lower subset} if \(\downarrow\!\! S=S\). An ordered \(\Omega\)-algebra \(\mathcal{A}= (A,\Omega_{\mathcal{A}}, \leq_{\mathcal{A}})\) is called a \textit{sup-algebra} if the poset \((A, \leq_{\mathcal{A}} )\) is a complete lattice and all elementary translations preserve joins. Denoting
Xia Zhang, Valdis Laan, Jianjun Feng
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Essential extensions and the injective hull

Lecture Notes in Mathematics, 1967
Carl Faith
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Injective hulls are not natural

Algebra Universalis, 2002
The question whether a given category has enough injectives (so that every object may be embedded into an injective one) or even injective hulls (so that such embeddings may be chosen to be essential), has been investigated for many categories, particularly in commutative and homological algebra, algebraic geometry, topology and in functional analysis.
Adámek, Jiří, Herrlich, Horst, Rosický, Jiří, Tholen, Walter   +3 more
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Injective Hulls of Semilattices

Canadian Mathematical Bulletin, 1970
A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relationdefines a partial ordering of S.
Bruns, G., Lakser, H.
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Injective hulls of chains

Archiv Der Mathematik, 1973
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Injective Hulls in POSV

Results in Mathematics, 1999
The known results about injective objects in the category of join semilattices are generalized to the category \(\text{POS}_V\) of posets and \(V\)-homomorphisms. Any \(V\)-homomorphism is isotone and, on join semilattices, \(V\)-homomorphisms coincide with join preserving maps.
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On the Annihilators of the Injective Hull of a Module

Canadian Mathematical Bulletin, 1969
In [2, page 151], J. Lambek proposes the following exercise: With any maximal right ideal M of a ring R with 1 associate the ideal . Show that OM, is the right annihilator of the injective hull of the right R-module R/M. The purpose of this note is to show that the above statement is true for a much larger class of right ideals than that of maximal ...
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Constructing pure injective hulls

Journal of Symbolic Logic, 1980
Let A be an abelian group and B a pure injective pure extension of A. Then there is a homomorphic image C of B over A which is a pure injective hull of A; C can be constructed by using Zorn's lemma to find a suitable congruence on B. In a paper [4] which greatly generalises this and related facts about pure injectives, Walter Taylor asks (Problem 1.5 ...
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