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#### Recent Posts:

- The Multiplicity of an Affine Plane Curve at a Point
- Simple and Multiple Points of Affine Plane Curves
- Affine Plane Curves
- Polynomial Forms
- Discrete Valuation Rings
- Local Rings
- The Rational Function Field of an Affine Variety
- 7972
- The Coordinate Ring of an Affine Variety
- Affine Varieties
- Corollary to the Hilbert Basis Theorem
- The Hilbert Basis Theorem
- Noetherian Rings
- The Ideal of a Set of Points Review
- The Ideal of a Set of Points is a Radical Ideal
- Basic Properties of the Ideal of a Set of Points
- The Ideal of a Set of Points
- Affine Algebraic Sets Review
- Basic Properties of Affine Algebraic Sets
- Affine Algebraic Sets
- Affine n-Space over a Field
- The Generalized Fundamental Theorem of Projective Planes
- The Fundamental Theorem of Projective Planes
- Product Collineations of Projective Planes
- Inverse Collineations of Projective Planes
- Identity Collineations of Projective Planes
- The Preservation of Collinear Points and Concurrent Lines with Collineations
- Collineations of Projective Planes on Lines
- Collineations of Projective Planes on Points
- Projective Planes in the Finite Field Zp
- The Fano Plane
- The Intersection of Two Distinct Lines in the Real Projective Plane
- The Existence of a Unique Point Through Two Distinct Lines in the Real Projective Plane
- The Equation of the Line Passing Through Two Distinct Points in the Real Projective Plane
- The Existence of a Unique Line Through Two Distinct Points In The Real Projective Plane
- Lines in the Real Projective Plane
- The Real Projective Plane
- Collinear Points and Concurrent Lines
- Linear Independence and Dependence
- Vector Spaces
- Parallel and Perpendicular Lines
- The Midpoint Between Two Points
- The Distance Between Two Points
- The Slope Intercept and General Forms of a Line
- Horizontal and Vertical Lines
- Finding Points of Intersection of Two Lines
- Finding the Interception Points of a Line
- Interception Points of a Line
- Solving 1-Variable Linear Equations
- The Minkowski (Gauge) Functional
- Absorbent Sets
- Absolutely Convex Sets
- Amenability of Abelian Groups
- ℓ^1(G) is Amenable if and only if G is an Amenable Group 2
- ℓ^1(G) is Amenable if and only if G is an Amenable Group 1
- Amenable Groups and Amenable Banach Algebras
- Inner Bounded X-Derivations, B1(A, X)
- Bounded X-Derivations, Z1(A, X)
- For Semi-Simple Commutative Banach Algebras A and B – A⊗B is Semi-Simple
- For Commutative Banach Algebras A and B over C – ΦA×ΦB is Homeomorphic to ΦA⊗pB
- The Algebraic Tensor Product of Two Normed Algebras
- Embedding Subspaces A of BL(X) and B of BL(Y) Into BL(X⊗pY)
- Cross Norms on X⊗Y
- Tensor Products of Linear Operators of Normed Linear Spaces
- ℓ1⊗pX is Isometrically Isomorphic to ℓ1(X) for Banach Spaces X
- The Closed Unit Ball of X⊗pY
- (X⊗pY)* and BL(X, Y; F) are Isometrically Isomorphic
- Alternative Definitions of the Projective Tensor Norm on X⊗Y
- The Projective Tensor Product of X⊗Y
- The Weak Tensor Product of X⊗Y
- The Trace Linear Functional on X*⊗X
- The Existence of a Linear Map σ on X⊗Y to Z that Matches a Bilinear Map on X×Y to Z
- Tensor Products with Direct Sums of Normed Linear Spaces
- Criteria for a Tensor u in X⊗Y to be 0
- X⊗Y and Y⊗X are Isomorphic Linear Spaces
- Linear Independence Properties of Tensor Products of Normed Linear Spaces
- Properties of Elementary Tensors of Normed Linear Spaces
- The Algebraic Tensor Product of Two Normed Linear Spaces
- Examples of Bilinear Mappings
- Bilinear Mappings and n-Linear Mappings
- Continuity of a Homomorphism from a Commutative Banach Algebra to a Semi-Simple Commutative Banach Algebra
- Semi-Simple Commutative Banach Algebras
- The Radical of a Commutative Banach Algebra
- The Gelfand Representation of a Commutative Banach Algebra
- The Carrier Space of a Commutative Banach Algebra
- The Spectrum of an Element in a Commutative Banach Algebra over C
- Equivalent Criterion for a Linear Functional to be Multiplicative in a Banach Algebra
- Jordan Functionals on a Banach Algebra
- Characterization of Maximal Modular Two-Sided Ideals in a Commutative Banach Algebra over C
- Characterization of Maximal Modular Two-Sided Ideals of Codimension 1 in a Banach Algebra over C
- The Gelfand-Mazur Theorem
- For Algebras A – ker(f) is a Two-Sided Ideal of A for all Multiplicative Linear Functionals f
- For Algebras with Unit A – ker(f) ⊆ Sing(A) for all Multiplicative Linear Functionals f
- Multiplicative Linear Functionals on a Banach Algebra
- Conditions for a Complex Banach Algebra with Unit to be Commutative
- The Spectrum of an Element in a Maximal Commutative Subset of an Algebra
- Maximal Commutative Subsets of an Algebra
- Commutative Subsets of an Algebra
- Approximate Identities in A for X when X is a Banach Left A-Module 4
- Approximate Identities in A for X when X is a Banach Left A-Module 3