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math.RA2023
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…
math.RA2023
Products of Traceless and Semi-Traceless Matrices over Division Rings and their Applications
Peter V. Danchev, Truong Huu Dung, Tran Nam Son
We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give so…
math.RA2015
Generalized algebraic rational identities of subnormal subgroups in division rings
Bui Xuan Hai, Mai Hoang Bien, Truong Huu Dung
In this note, we introduce a new concept of a {\it generalized algebraic rational identity} to investigate the structure of division rings. The main theorem asserts that if a non-c…