Similarity of certain abelian collineation groups of a translation plane corresponds to strong isotopy of multiplication variations of a commutative semifield. Strong isotopy of Dickson semifields and their multiplication variations is characterized. The splitting of the isotopy class of a Dickson semifield over different types of basic fields (e. g. absolutely algebraic fields, number fields) into classes of strong isotopy is investigated. **
1991 Mathematics Subject Classification
17A35 51J99 17A36 51A40
commutative division algebra Dickson semifield strong isotopism affine incidence group
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