 -primary component VII page
-primary module VII page
Abelian closure V page
Abelian extension V page
Absolutely semi-simple endomorphism VII page
Addition of inequalities VI page
Adjunction (extension obtained by) V page
Algebraic closure V page
Algebraic element in an algebra V page
Algebraic extension V page
Algebraic number V page
Algebraically closed field V page
Algebraically dependent family, subset V page
Algebraically disjoint extensions V page
Algebraically free family of extensions V page
Algebraically free family, subset IV page V page
Archimedean ordered group VI page exercise
Artin — Schreier theorem VI page
Artin — Schreier theory V page
Artin’s theorem V page
Associated elements VI page
Bezout’s identity VII page
Budan — Fourier rule VI page exercise
Characteristic exponent of a field V page
Characteristic of a ring V page
Characteristic submodule VII page exercise
Chinese remainder theorem VI page exercise
Closed (field, algebraically) V page
Closed (field, separably) V page
Closed (relatively algebraically) field V page
Closed half-line VI page
Closure (abelian) of a field V page
Closure (algebraic separable) V page
Closure (algebraic) of a field V page
Closure (perfect) V page
Closure (relative algebraic) V page
Closure (relative p-radical) V page
Closure (relative separable algebraic) V page
Coefficients of a formal power series IV page
Coefficients of a polynomial IV page
Compatible (order relation) with a group, monoid structure VI page
Compatible (order relation) with a ring structure VI page
Compatible (preorder relation) with a commutative monoid structure VI page
Complementary orientation VI page
Composite extension V page
Composition of series IV page exercise
Conjugacy class in  V page
Conjugate elements V page
Conjugate extensions V page
Constant polynomial, term IV page
Content VII page
Coprime elements VI page
Coproduct in TS(M) IV page
Cubic extension V page
Cyclic extension V page
Cyclic vector space (for u) VII page
Cyclotomic extension V page
Cyclotomic polynomial V page
Decomposable module VII page
Decomposition algebra (universal) of a polynomial IV page
Decomposition theorem VI page
Dedekind’s theorem V page
Degree (inseparable) of an extension V page
Degree (separable) of an extension V page
Degree (total) of a polynomial IV page
Degree (total) of a rational fraction IV page
Degree of an algebra over a field V page
Degree of an algebraic element V page
Derivation (partial) in a p-radical extension of height =s 1 V page
Derivative (partial) of a formal power series IV page
Derivative (partial) of a polynomial IV page
Descartes’rule VI page exercise
Diagonal, diagonalizable set of endomorphisms VII page
Diagonalizable, diagonalized algebra V page
Direct basis VI page
Direction of a half-line VI page
Direction vector VI page
Discriminant of a monic polynomial IV page
Discriminant of a polynomial IV page
Discriminant of a sequence of elements V page
Disjoint (algebraically) extensions V page
Disjoint (linearly) extensions V page
Divided power in TS(M) IV page
Divided power of a series IV page exercise
Divisibility relation VI page
Division (euclidean) IV page
Divisor (greatest common) IV page VI page
Divisor of an element VI page
Divisors (elementary) of a module VII page
Double root IV page
Eigenspace VII page
Eigenvalue VII page
Elementary divisor of a module VII page
Elementary symmetric polynomial IV page
Etale algebra V page
Euclidean Domain VII page exercise
Euclid’s lemma VI page
Euler — Lagrange Theorem VI page
Euler’s identity VI page IV page exercise
Expansion at the origin of a rational fraction IV page V page
Exponential of a formal power series IV page
Exponential type (sequence of) IV page exercise
Extension (principle of) of algebraic identities IV page
Extension of a field V page
Finite extension V page
Finitely generated extension V page
Form of degree n IV page
Formal power series IV page
Formal power series (generalized) IV page
Fractions (fields of rational) IV page
Frobenius homomorphism V page V page
Galois extension V page
Galois group of an extension, of a polynomial V page
Galois theory V page
Gamma algebra of a module IV page exercise
Gaussian integer VII page
Generated (extension) V page
Generated (Galois extension) V page
Generated (quasi-Galois extension) V page
Generating family of an extension V page
Greatest common divisor (GCD) of elements VI page
Greatest common divisor of polynomials IV page
Greatest common divisor of principal ideals VII page
Half-line (closed, open) VI page
Half-lines (opposite) VI page
Hankel determinants IV page exercise
Height of a p-radical element V page
Height of a p-radical extension V page
Height of an element of K(T) V page exercise
Hermite interpolation formula IV page exercise
Hermite reduced form VII page exercise
Homogeneous component of a formal power series IV page
Imperfect field V page
Imperfection (degree of) V page exercise
Indecomposable module VII page
Indeterminate IV page
Index of a linear mapping V page
Indicator (Euler’s) V page
Indivisible element VII page
Inflation homomorphism V page
Inseparable degree V page
Integral ideal VI page
Invariant factors of a linear mapping VII page
Invariant factors of a module VII page
Invariant factors of a submodule VII page
Invariants (similarity) of an endomorphism VII page
Irreducible element VI page
Irreducible polynomial IV page
Isobaric polynomial IV page
Jordan decomposition VII page
| Jordan decomposition (multiplicative) VII page
Jordan Matrix VII page
Kummer extension V page exercise
Kummer theory V page
Lagrange interpolation formula IV page
Law (polynomial) IV page exercise
Leading coefficient IV page
Least common multiple (LCM) of elements VI page
Least common multiple of principal ideals VII page
Lefschetz’s principle V page
Lexicographic product of ordered groups VI page
Linear topology IV page
Linearly disjoint extensions V page
Linearly topologized algebra IV page
Logarithm of a formal power series IV page
Logarithmic derivative IV page
Luroth’s theorem V page exercise
Mac Laner’s criterion V page V page
Maximal ordered field VI page
Minimal polynomial of an element V page
Minimal polynomial of an endomorphism VII page
Minkowski’s lemma VII page exercise
Monic polynomial IV page
Monogenous extension V page
Monomials IV page
Multiple factor (polynomial without) IV page
Multiple of an element VI page
Multiple root IV page
Multiplicity (geometric) of an eigenvalue VII page
Multiplicity of a root IV page
Multiplicity of an elementary divisor VII page
Negative basis VI page
Negative element VI page
Negative n-vector VI page
Newton polygon V page exercise
Newton’s relations IV page IV page
Nilpotent component VII page
Norm V page
Normal basis, normal basis theorem V page
Normal extension V page
Open half-line VI page
Opposite half-lines VI page
Order of a (generalized) formal power series IV page IV page
Order of a root IV page
Orderable field VI page exercise
Ordered extension VI page
Ordered field VI page
Ordered group, monoid VI page
Ordered ring VI page
Orientation of a vector space VI page
Oriented affine space, vector space VI page
p-adic integers (ring of) V page
p-basis V page
p-basis (absolute) V page
p-free family V page
p-radical closure V page
p-radical element V page
p-radical extension IV page
p-torsion group VII page
Perfect closure of a ring V page
Perfect field V page
Perfect ring of characteristic p V page
Polynomial function IV page
Polynomial law IV page exercise
Polynomial mapping IV page
Polynomial mapping (homogeneous) IV page
Polynomial, polynomial algebra IV page
Positive basis VI page
Positive element VI page
Positive n-vector VI page
Power series (generalized formal) IV page IV page
Preordered group, monoid VI page
Primary extension V page
Prime field, subfield V page
Primitive element (theorem of the) V page
Primitive root of unity V page
Principal fractional ideal VI page
Principal ideal domain VII page
Principal ideal ring VII page exercise
Product (lexicographic) of ordered groups VI page
Product of ordered groups VI page
Product orientation VI page
Puiseux’s theorem V page exercise
Pure basis V page
Pure extension V page
Pure submodule VII page exercise
Pythagorean field VI page exercise
Quadratic extension V page
Quadratic reciprocity (theorem of) V page exercise
Quasi-Galois extension V page
Quotient in euclidean division IV page
Quotient orientation VI page
Rational fraction IV page
Rational function IV page
Reduced ring V page
Regular algebra V page
Regular extension V page
Relative algebraic closure of a field in an extension V page
Relatively algebraically closed field in an extension field V page
Relatively prime polynomials IV page
Remainder in euclidean division IV page
Representatives (system of) of irreducible elements VII page
Restriction homomorphism V page V page
Resultant of two polynomials IV page
Root of a polynomial IV page
Root of unity V page
Rule of signs VI page
Semi-simple (absolutely) component VII page
Semi-simple (absolutely) endomorphism VII page
Semi-simple endomorphism VII page
Semi-simple module VII page
Separable algebra V page
Separable algebraic closure (relative) V page
Separable algebraic extension V page
Separable closure V page
Separable degree V page
Separable element V page
Separable extension V page
Separable polynomial V page
Separably closed field V page
Separating transcendence basis V page
Series on E with values in F IV page exercise
Set ( -) V page
Sign of an element VI page
Similar endomorphisms, matrices VII page
Similarity invariants of on endomorpism VII page
Simple module VII page
Simple root IV page
Splitting field, extension V page
Subextension V page
Subfield V page
Substitutable element in a rational fraction IV page
Substitution in a formal power series IV page
Substitution in a polynomial IV page
Substitution in a rational fraction IV page
Symmetric (elementary) polynomials IV page
Symmetric formal power series IV page
Symmetric polynomial IV page
Symmetric product of symmetric tensors IV page
Symmetric rational fraction IV page
Symmetric tensor IV page
Symmetrized tensor IV page
Tangent linear mapping IV page
Taylor’s formula for formal power series IV page
Taylor’s formula for polynomials IV page
Term, constant term, of a formal power series IV page
Term, constant term, of a polynomial IV page
Trace V page
Transcendence basis V page
Transcendence degree V page
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