On distant-isomorphisms of projective lines
Copyright policy )On distant-isomorphisms of projective lines
We determine all distant-isomorphisms between projective lines over semilocal rings. In particular, for those semisimple rings that do not have a simple component which is isomorphic to a field, every distant isomorphism arises from a Jordan isomorphism of rings and a projectivity. We show this by virtue of a one-one correspondence linking the projective line over a semisimple ring with a Segre product of Grassmann spaces.
- Universität Hamburg Germany
- TU Wien Austria
Mathematics - Algebraic Geometry, 51C05, 51A10, 51A45, 17C50, Incidence structures embeddable into projective geometries, Homomorphism, automorphism and dualities in linear incidence geometry, Rings and Algebras (math.RA), Ring geometry (Hjelmslev, Barbilian, etc.), Jordan structures associated with other structures, FOS: Mathematics, Mathematics - Rings and Algebras, projective line over a ring, Algebraic Geometry (math.AG)
Mathematics - Algebraic Geometry, 51C05, 51A10, 51A45, 17C50, Incidence structures embeddable into projective geometries, Homomorphism, automorphism and dualities in linear incidence geometry, Rings and Algebras (math.RA), Ring geometry (Hjelmslev, Barbilian, etc.), Jordan structures associated with other structures, FOS: Mathematics, Mathematics - Rings and Algebras, projective line over a ring, Algebraic Geometry (math.AG)
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