3 citations · 13 across the 28 of their papers we have counts for
31 papers
Semi-Generalized co-Bassian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
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-Bassi…
Supper Bassian and Nearly Generalized Bassian Abelian Groups
Peter Danchev, Brendan Goldsmith
In connection to two recent publications of ours in Arch. Math. Basel (2021) and Acta Math. Hung. (2022), respectively, and in regard to the results obtained in Arch. Math. Basel (…
Images of Multilinear Polynomials on Generalized Quaternion Algebras
Peter Vassilev Danchev, Truong Huu Dung, Tran Nam Son
The main goal of this paper is to extend [J. Algebra Appl. 20 (2021), 2150074] to generalized quaternion algebras, even when these algebras are not necessarily division rings. More…
Semi-Generalized Bassian Groups
Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef
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 comprehens…
Generalized Bassian and other Mixed Abelian Groups with Bounded p-Torsion
Peter V. Danchev, Patrick W. Keef
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 k…
Rings whose Nil-Clean and Clean Elements are Uniquely Nil-Clean
Jian Cui, Peter Danchev, Danya-Jin
We consider and study those rings in which each nil-clean or clean element is uniquely nil-clean. We establish that, for abelian rings, these rings have a satisfactory description…