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11 papers
Algebraic aspects of general free skew extensions of rings
Vitor O. Ferreira, Érica Z. Fornaroli, Javier Sánchez
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different…
Free symmetric and unitary pairs in the field of fractions of torsion-free nilpotent group algebras
Vitor O. Ferreira, Jairo Z. Goncalves, Javier Sanchez
Let be a field of characteristic different from and let be a nonabelian residually torsion-free nilpotent group. It is known that is an orderable group. Let …
Free algebras in division rings with an involution
Vitor O. Ferreira, Érica Z. Fornaroli, Jairo Z. Gonçalves
Some general criteria to produce explicit free algebras inside the division ring of fractions of skew polynomial rings are presented. These criteria are applied to some special cas…
Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras
Vitor O. Ferreira, Jairo Z. Gonçalves, Javier Sánchez
For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring D(L) constructed by Lichtman. If U(L) is an Ore domain, D(L) coincides…
Free symmetric and unitary pairs in division rings infinite-dimensional over their centers
Vitor O. Ferreira, Jairo Z. Goncalves
Let be a division ring infinite-dimensional over its center with multiplicative group . We show that if belongs to certain families, there exist free symmet…
Free symmetric group algebras in division rings generated by poly-orderable groups
Vitor O. Ferreira, Jairo Z. Goncalves, Javier Sanchez
We show that the canonical involution on a nonabelian poly-orderable group G extends to the Hughes-free division ring of fractions D of the group algebra k[G] of G over a field k a…