The structure of perfect fields
Duong Quoc Viet, Truong Thi Hong Thanh
TL;DR
This paper characterizes the structure of perfect fields in positive characteristic, demonstrating that any such field is an algebraic extension of a fundamental perfect field, thereby clarifying their foundational structure.
Contribution
It introduces the concept of fundamental perfect fields and proves that all perfect fields of positive characteristic are algebraic extensions of these fundamental fields.
Findings
Characterization of perfect fields as algebraic extensions of fundamental perfect fields
Construction of fundamental perfect fields in positive characteristic
Proof that all perfect fields of positive characteristic derive from fundamental perfect fields
Abstract
This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental perfect field.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Equations and Dynamical Systems