4 papers
Parametric decompositions into products of involutions
Gaofeng Huang, Frank Kutzschebauch, Tran Nam Son +1
It is a well-known result of Gustafson, Halmos and Radjavi, dating back to 1976, that any matrix in is a product of at most 4 involutions. We consider a natu…
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…
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…
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…