The Hölder Rigidity Theorem for Valuations

M. H. Hosseini

Department of Mathematics, Birjand University, P. O. Box 11111, Birjand, IRAN.


In 1999 Garsia proved Hölder rigidity theorem for absolute4. In this papers we study generalized valuation on a field or a commutative ring with unit element satisfying an approximate maximize inequality an approximate multiplicative property. Also we prove Hölder rigidity theorem for valuations on ring, that they are always Hölder equivalent to a classical valuations.

Keywords :Valuation, (C1, C2) Hölder valuation, (C0 ,α ) -Hölder equivalent, Hölder rigidity.

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