Topological Rings of Endomorphisms

Ursul, Mihail; Juráš, Martin

doi:10.1080/00927870902936950

Cited by 4 publications

(5 citation statements)

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“…Examples of abelian groups A such that J(EndA) is not closed were constructed independently in [5] and [15]. Moreover, in [15] an example of an abelian group A was presented as a direct sum of cyclic groups such that the Jacobson radical J(EndA) is not closed. These examples raise the following question: Question 1.…”

Section: The Finite and The Liebert Topologies On Endomorphism Rings ...mentioning

confidence: 99%

“…We construct as in [15] examples such that J(EndA) is not closed for certain groups A that are direct sums of cyclic groups.…”

Section: Introductionmentioning

confidence: 99%

“…But there is a well-known example in Bourbaki for a free module M R where J(End(M R )) is not closed ( [4], Chapter III, § 6, p. 110). The proof essentially uses the properties of R. The first examples of abelian groups A with non-closed J(EndA) were constructed in [15] and [5].…”

Section: Introductionmentioning

confidence: 99%

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On the endomorphism rings of abelian groups and their Jacobson radical

Bovdi

Grishkov²,

Ursul

2015

Period Math Hung

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We give a characterization of those abelian groups which are direct sums of cyclic groups and the Jacobson radical of their endomorphism rings are closed. A complete characterization of p-groups A for which (EndA, T L ) is locally compact, where T L is the Liebert topology on EndA, is given. We prove that if A is a countable elementary p-group then EndA has a non-admissible ring topology. To every functorial topology on A a right bounded ring topology on EndA is attached. By using this topology we construct on EndA a non-metrizable and non-admissibe ring topology on EndA for elementary countable p-groups A.1991 Mathematics Subject Classification. Primary: 16W80, 16A65, 16S50, 16N40.Key words and phrases. topological ring, Jacobson radical, quasi-injective module, endomorphism ring, admissible topology, Bohr topology, Liebert topology, finite topology, functorial topology, shift homomorphism.The research was supported by FAPESP (Brazil) Process N: 2014/18318-7, CNPq (Brazil) and RFFI (Russia) 13-01-00239a.

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Section: The Finite and The Liebert Topologies On Endomorphism Rings ...mentioning

confidence: 99%

“…We construct as in [15] examples such that J(EndA) is not closed for certain groups A that are direct sums of cyclic groups.…”

Section: Introductionmentioning

confidence: 99%

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On the endomorphism rings of abelian groups and their Jacobson radical

Bovdi

Grishkov²,

Ursul

2015

Period Math Hung

Self Cite

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“…A group is called Abelian if the composition is commutative, generating normal subgroups in every case [4]. However, not all Abelian groups inherit any endomorphic ring within compact ring topology [4,5]. Moreover, an Abelian group can be constructed considering open J-radicals (Jacobson radicals) in a ring topology, which is finite [5].…”

Section: Introductionmentioning

confidence: 99%

“…However, not all Abelian groups inherit any endomorphic ring within compact ring topology [4,5]. Moreover, an Abelian group can be constructed considering open J-radicals (Jacobson radicals) in a ring topology, which is finite [5]. The normed ring structures are the generalization of commutative rings.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces

Bagchi

2019

Symmetry

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The concepts of fuzzy sets and topology are widely applied to model various algebraic structures and computations. The dynamics of fuzzy measures in topological spaces having distributed monoid embeddings is an interesting topic in the presence of topological endomorphism. This paper presents the analysis of topological endomorphism and the properties of topological fuzzy measures in distributed monoid spaces. The topological space is considered to be Hausdorff and second countable in nature. The analysis of consistency of fuzzy measure in endomorphic topological spaces is formulated. The algebraic structures of endomorphic topological spaces having distributed cyclic monoids are constructed. The cyclic monoids contain specific generators, and a related cyclic topological endomorphism within the subspace is formulated. The analytical properties of fuzzy topological measures in the presence of cyclic topological endomorphism are presented. A comparative analysis of this proposed work with other related work in the domain is included.

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Torsion-complete and algebraically compact groups with compact endomorphism rings

Ursul

2017

Communications in Algebra

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Topological Rings of Endomorphisms

Cited by 4 publications

References 2 publications

On the endomorphism rings of abelian groups and their Jacobson radical

On the endomorphism rings of abelian groups and their Jacobson radical

Analysis of Topological Endomorphism of Fuzzy Measure in Hausdorff Distributed Monoid Spaces

Torsion-complete and algebraically compact groups with compact endomorphism rings

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