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pro vyhledávání: '"Keef, Patrick"'
This paper targets to generalize the notion of Hopfian groups in the commutative case by defining the so-called {\bf relatively Hopfian groups} and {\bf weakly Hopfian groups}, and establishing some their crucial properties and characterizations. Spe
Externí odkaz:
http://arxiv.org/abs/2408.01277
Trying to finalize in some way the present subject, this paper targets to generalize substantially the notions of Bassian and co-Bassian groups by introducing the so-called finitely (co-)Bassian groups, semi (co-)Bassian groups, fully generalized (co
Externí odkaz:
http://arxiv.org/abs/2403.08096
As a common non-trivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically, we give a
Externí odkaz:
http://arxiv.org/abs/2310.00765
As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehensive investigation. Precisely, we give a satisfactory characterization
Externí odkaz:
http://arxiv.org/abs/2308.13948
Autor:
Danchev, Peter V., Keef, Patrick W.
It is known that a mixed abelian group G with torsion T is Bassian if, and only if, it has finite torsion-free rank and has finite p-torsion (i.e., each Tp is finite). It is also known that if G is generalized Bassian, then each pTp is finite, so tha
Externí odkaz:
http://arxiv.org/abs/2308.00641
Autor:
Danchev, Peter V., Keef, Patrick W.
For Abelian p-groups, Goldsmith, Salce, et al., introduced the notion of minimal full inertia. In parallel to this, we define the concept of minimal characteristic inertia and explore those p-primary Abelian groups having minimal characteristic inert
Externí odkaz:
http://arxiv.org/abs/2211.05204
Autor:
Danchev, Peter V., Keef, Patrick W.
Publikováno v:
In Journal of Algebra 1 February 2025 663:1-19
We study some close relationships between the classes of transitive, fully transitive and Krylov transitive torsion-free Abelian groups. In addition, as an application of the achieved assertions, we resolve some oldstanding problems, posed by Krylov-
Externí odkaz:
http://arxiv.org/abs/2110.04646
Akademický článek
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Autor:
Keef, Patrick, Salce, Luigi
Publikováno v:
In Journal of Pure and Applied Algebra April 2023 227(4)