Abhyankar's inequality is an inequality involving extensions of
valued fields in
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
, introduced by .
Abhyankar's inequality states that for an extension ''K''/''k'' of
valued fields, the
transcendence degree of ''K''/''k'' is at least the
transcendence degree of the
residue field extension plus the rank of the
quotient of the
valuation group In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size in ...
s; here the rank of an abelian group
is defined as
.
References
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Field (mathematics)
Commutative algebra
Theorems in abstract algebra
{{commutative-algebra-stub