Fully Inert Subgroups of Completely Decomposable Groups with Homogeneous Components of Finite Rank

Autor: A. R. Chekhlov

Publikováno v: Russian Mathematics. 66:82-90

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c2920975dbf4495862d3cedfe5ca38c6
https://doi.org/10.3103/s1066369x22120015

ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS

Autor: Grigore Călugăreanu, Andrey R. Chekhlov

Publikováno v: Volume: 30, Issue: 30 217-230
International Electronic Journal of Algebra
International electronic journal of algebra. 2021. Vol. 30. P. 217-230

A ring $R$ is called left comorphic if for every $a\in R$ there exists $b\in R$ such that the left and right annihilators satisfy $Ra=l(b)$ and $r(a)=bR$. In this paper, the Abelian groups with left comorphic endomorphism rings are completely determi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9c27788d425ef3a8aed905b69a389640
https://doi.org/10.24330/ieja.969907

Generalizations of fully transitive and valuated Abelian p-groups

Autor: Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef

Publikováno v: Journal of algebra. 2021. Vol. 566. P. 187-204

If H is a subgroup of an Abelian p-group G, we say G is H-fully transitive if using the height valuation from G, for every x ∈ H , every valuated (i.e., non-height decreasing) homomorphism 〈 x 〉 → G extends to a valuated homomorphism H → G

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b364822ed1055db7e686793664c08fa
https://doi.org/10.1016/j.jalgebra.2020.09.014

ON PROJECTIVELY INERT SUBGROUPS OF COMPLETELY DECOMPOSABLE FINITE RANK GROUPS

Autor: Olesya V. Ivanets, Andrey R. Chekhlov

Publikováno v: Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika. :63-68

Let a group G be a finite direct sum of torsion-free rank 1 groups Gi. It is proved that every projectively inert subgroup of G is commensurate with a fully invariant subgroup if and only if all Gi are not divisible by any prime number p, and for dif

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https://doi.org/10.17223/19988621/67/6

Universally fully and Krylov transitive torsion-free abelian groups

Autor: Peter V. Danchev, Patrick W. Keef, Andrey R. Chekhlov

Publikováno v: Monatshefte für Mathematik. 2022. Vol. 198, № 3. P. 517-534

Extending results from our recent paper in Chekhlov et al. (J Algebra 566(2):187–204, 2021), we define and explore the classes of universally fully transitive and universally Krylov transitive torsion-free Abelian groups. A characterization theorem

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c311d3fb456afc3fc1a238ebca67241
https://vital.lib.tsu.ru/vital/access/manager/Repository/koha:000997860