6533b862fe1ef96bd12c61dc
RESEARCH PRODUCT
On the group of the automorphisms of some algebraic systems
Giancarlo TeppatiRenato AscoliGiuseppina Brunosubject
AlgebraGeneral MathematicsUniversal algebraAlgebraic geometryAlgebraic numberAlgebraically closed fieldQuaternionAutomorphismBurnside theoremMathematicsVector spacedescription
Within a framework of general algebra we firstly formulate a proposition on the group of the automorphisms of some irreducible algebrae (id est algebrae without proper non trivial subalgebrae). This proposition includes as particular cases the uniqueness of the automorphisms of the rational field and the Burnside theorem on the commutant of an irreducible set of operators of a finite dimensional vector space over an algebraically closed field. Afterwards we apply the general proposition to modules with irreducible sets of semilinear operators and we obtain a theorem which generalises from several points of view the Burnside theorem. Finally we derive as an application a proposition which specifies the set of the Hermitian operators that commute with an irreducible set of semilinear operators of a finite dimensional real, complex or quaternion scalar product space.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1968-01-01 | ANNALI DELL UNIVERSITA DI FERRARA |