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On Ring Properties of Injective Hulls
Canadian Mathematical Bulletin, 1975Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense.It is known that is a regular ring (in the sense of von Neumann) if and only if ...
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Injective Hulls in the Category of Mildly Distributive Semilattices
Order, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rings whose Injective Hulls are Cogenerators
Acta Mathematica Hungarica, 1998Let \(R\) be an associative ring with \(1\), and assume that \(R\) is right noetherian. The authors give necessary and sufficient conditions under which \(R\) is right artinian, in terms of the existence of nonzero linear maps from an arbitrary nonzero (right) \(R\)-module into a projective or flat module. This paper is motivated by similar results of \
Wu, Zhixiang, Xu, Yonghua
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Rings with cyclic injective hulls
Communications in Algebra, 2020We study the rings R whose injective hull E(RR) is cyclic, extending and simplifying many of the known results on the subject, and obtaining new ones.
Yasser F. Ibrahim, Mohamed F. Yousif
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ALGEBRAIC HULLS OF ADJOINT FUNCTORS AS INJECTIVE HULLS
Quaestiones Mathematicae, 1997Abstract For each adjoint functor U: A → X where X is an (ϵ, M)-category having enough ϵ-projectives, we construct an (ϵ, M)-algebraic hull E: (A, U) → (Â, U), i.e., (Â, U) is (epsiv; M)-algebraic and E has a certain denseness property. We show that there is a conglomerate of functors over X with respect to which the (ϵ M)-algebraic categories are ...
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Endomorphisms of the Quasi-Injective Hull of a Module
Canadian Mathematical Bulletin, 1970R is a ring and M is a right R-module for which Rl = {m ∊ M | mR = 0} is the zero submodule. Let and be the injective hull and the quasi-injective hull of M respectively. Then where [1]. The ring plays an important role, in many cases, in the studying of R especially when D is a division ring. For x ∊ M, we denote the annihilator of x in R by xγ =
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The pure-injective and RD-injective hulls of a ring
Mathematical Notes, 1992\textit{A. Facchini} proved [Q. J. Math., Oxf. II. Ser. 39, 307-321 (1988; Zbl 0668.13012)] that if \(R\) is a commutative ring and if the pure- injective hull of \(R\) (as a module over itself) is indecomposable then \(R\) is local and he asked if the converse is true.
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Injective Hulls of C ∗ Algebras
Transactions of the American Mathematical Society, 1968openaire +1 more source