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- W2953008298 abstract "In this paper we prove relationships between two generalizations of commutative valuation theory for noncommutative central simple algebras: (1) Dubrovin valuation rings; and (2) the value functions called gauges introduced by Tignol and Wadsworth in [TW1] and [TW2]. We show that if v is a valuation on a field F with associated valuation ring V and v is defectless in a central simple F-algebra A, and C is a subring of A, then the following are equivalent: (a) C is the gauge ring of some minimal v-gauge on A, i.e., a gauge with the minimal number of simple components of C/J(C); (b) C is integral over V with C = B_1 cap ... cap B_xi$ where each B_i is a Dubrovin valuation ring of A with center V, and the B_i satisfy Graeter's Intersection Property. Along the way we prove the existence of minimal gauges whenever possible and we show how gauges on simple algebras are built from gauges on central simple algebras." @default.
- W2953008298 created "2019-06-27" @default.
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- W2953008298 date "2013-07-21" @default.
- W2953008298 modified "2023-09-27" @default.
- W2953008298 title "Value Functions and Dubrovin Valuation Rings on Simple Algebras" @default.
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