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Journal of Algebra and Its Applications, 2014
A ring is right tall if every non-noetherian right module contains a proper non-noetherian submodule. We prove a ring-theoretical criterion of tall commutative rings. Besides other examples which illustrate limits of proven necessary and sufficient conditions, we construct an example of a tall commutative ring that is non-max.
Penk, Tomáš, Žemlička, Jan
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A ring is right tall if every non-noetherian right module contains a proper non-noetherian submodule. We prove a ring-theoretical criterion of tall commutative rings. Besides other examples which illustrate limits of proven necessary and sufficient conditions, we construct an example of a tall commutative ring that is non-max.
Penk, Tomáš, Žemlička, Jan
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Commutative Endomorphism Rings
Canadian Journal of Mathematics, 1971The problem of classifying the torsion-free abelian groups with commutative endomorphism rings appears as Fuchs’ problems in [ 4 , Problems 46 and 47]. They are far from solved, and the obstacles to a solution appear formidable (see [ 4; 5 ]).
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Canadian Journal of Mathematics, 1982
Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to provide two new characterizations of coherent rings. The first of these characterizations shows that the class of coherent rings is precisely the class of rings for which certain duality homomorphisms are isomorphisms.
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Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to provide two new characterizations of coherent rings. The first of these characterizations shows that the class of coherent rings is precisely the class of rings for which certain duality homomorphisms are isomorphisms.
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Acta Mathematica Hungarica, 2002
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Bell, H. E., Klein, A. A.
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Bell, H. E., Klein, A. A.
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Commutative Self-Injective Rings
Canadian Journal of Mathematics, 1970All rings considered here are commutative containing at least two elements, but may not have identity. A ring R is said to be selfinjective if R as an R-module is injective. A ring R is said to be pre-selfinjective if every proper homomorphic image of R is ...
Singh, S., Wasan, K.
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Metaideals in Commutative Rings
Algebra Colloquium, 2005New examples of metaideals in commutative rings are constructed. It is proved that metaideals of a commutative ring form a sublattice of the lattice of all subrings, and for any subring A of a commutative ring P, there exists the largest subring Mid P (A) (called metaidealizer) in which A is a metaideal. Metaidealizers in several cases are described.
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On Commutative Splitting Rings
Proceedings of the London Mathematical Society, 1970Abstract not ...
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Commutative consistently $$L^{*}$$-rings
Algebra universalis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematics of the USSR-Sbornik, 1976
This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes ...
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This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes ...
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