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• Kernel_(algebra) abstract "In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a linear map. The kernel of a matrix, also called the null space, is the kernel of the linear map defined by the matrix.The definition of kernel takes various forms in various contexts. But in all of them, the kernel of a homomorphism is trivial (in a sense relevant to that context) if and only if the homomorphism is injective. The fundamental theorem on homomorphisms (or first isomorphism theorem) is a theorem, again taking various forms, that applies to the quotient algebra defined by the kernel.In this article, we first survey kernels for some important types of algebraic structures; then we give general definitions from universal algebra for generic algebraic structures.".
• Kernel_(algebra) wikiPageID "45240".
• Kernel_(algebra) wikiPageLength "15208".
• Kernel_(algebra) wikiPageOutDegree "130".
• Kernel_(algebra) wikiPageRevisionID "679812653".
• Kernel_(algebra) wikiPageWikiLink Abelian_categories.
• Kernel_(algebra) wikiPageWikiLink Abelian_category.
• Kernel_(algebra) wikiPageWikiLink Abelian_group.
• Kernel_(algebra) wikiPageWikiLink Abstract_algebra.
• Kernel_(algebra) wikiPageWikiLink Algebra_over_a_field.
• Kernel_(algebra) wikiPageWikiLink Algebraic_structure.
• Kernel_(algebra) wikiPageWikiLink Basis_(linear_algebra).
• Kernel_(algebra) wikiPageWikiLink Bimodule.
• Kernel_(algebra) wikiPageWikiLink Category:Algebra.
• Kernel_(algebra) wikiPageWikiLink Category:Isomorphism_theorems.
• Kernel_(algebra) wikiPageWikiLink Category:Linear_algebra.
• Kernel_(algebra) wikiPageWikiLink Category_theory.
• Kernel_(algebra) wikiPageWikiLink Closed_set.
• Kernel_(algebra) wikiPageWikiLink Codomain.
• Kernel_(algebra) wikiPageWikiLink Commutative_group.
• Kernel_(algebra) wikiPageWikiLink Congruence_relation.
• Kernel_(algebra) wikiPageWikiLink Continuous_function.
• Kernel_(algebra) wikiPageWikiLink Continuous_map.
• Kernel_(algebra) wikiPageWikiLink Difference_kernel.
• Kernel_(algebra) wikiPageWikiLink Differentiable_function.
• Kernel_(algebra) wikiPageWikiLink Differential_operator.
• Kernel_(algebra) wikiPageWikiLink Dimension_(linear_algebra).
• Kernel_(algebra) wikiPageWikiLink Dimension_(vector_space).
• Kernel_(algebra) wikiPageWikiLink Direct_product.
• Kernel_(algebra) wikiPageWikiLink Division_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Equaliser_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Equality_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Equalizer_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Equivalence_class.
• Kernel_(algebra) wikiPageWikiLink Equivalence_relation.
• Kernel_(algebra) wikiPageWikiLink Finite-dimensional_vector_space.
• Kernel_(algebra) wikiPageWikiLink First_isomorphism_theorem.
• Kernel_(algebra) wikiPageWikiLink Function_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Fundamental_theorem_on_homomorphisms.
• Kernel_(algebra) wikiPageWikiLink Group_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Group_homomorphism.
• Kernel_(algebra) wikiPageWikiLink Hausdorff_space.
• Kernel_(algebra) wikiPageWikiLink Homogeneous_differential_equation.
• Kernel_(algebra) wikiPageWikiLink Homomorphism.
• Kernel_(algebra) wikiPageWikiLink Ideal_(ring_theory).
• Kernel_(algebra) wikiPageWikiLink Identity_element.
• Kernel_(algebra) wikiPageWikiLink Image_(function).
• Kernel_(algebra) wikiPageWikiLink Image_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Injective_function.
• Kernel_(algebra) wikiPageWikiLink Isomorphism_theorem.
• Kernel_(algebra) wikiPageWikiLink Kernel_(category_theory).
• Kernel_(algebra) wikiPageWikiLink Kernel_(linear_algebra).
• Kernel_(algebra) wikiPageWikiLink Kernel_(matrix).
• Kernel_(algebra) wikiPageWikiLink Kernel_(set_theory).
• Kernel_(algebra) wikiPageWikiLink Kernel_of_a_function.
• Kernel_(algebra) wikiPageWikiLink Kernel_pair.
• Kernel_(algebra) wikiPageWikiLink Linear_map.
• Kernel_(algebra) wikiPageWikiLink Linear_subspace.
• Kernel_(algebra) wikiPageWikiLink Malcev_algebra.
• Kernel_(algebra) wikiPageWikiLink Mathematics.
• Kernel_(algebra) wikiPageWikiLink Matrix_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Module_(algebra).
• Kernel_(algebra) wikiPageWikiLink Module_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Monoid.
• Kernel_(algebra) wikiPageWikiLink Monoid_(algebra).
• Kernel_(algebra) wikiPageWikiLink Monoid_homomorphism.
• Kernel_(algebra) wikiPageWikiLink Natural_isomorphism.
• Kernel_(algebra) wikiPageWikiLink Natural_transformation.
• Kernel_(algebra) wikiPageWikiLink Neutral_element.
• Kernel_(algebra) wikiPageWikiLink Normal_subgroup.
• Kernel_(algebra) wikiPageWikiLink Null_ring.
• Kernel_(algebra) wikiPageWikiLink Ordered_pair.
• Kernel_(algebra) wikiPageWikiLink Preimage.
• Kernel_(algebra) wikiPageWikiLink Quotient.
• Kernel_(algebra) wikiPageWikiLink Quotient_algebra.
• Kernel_(algebra) wikiPageWikiLink Quotient_group.
• Kernel_(algebra) wikiPageWikiLink Quotient_monoid.
• Kernel_(algebra) wikiPageWikiLink Quotient_ring.
• Kernel_(algebra) wikiPageWikiLink Quotient_space_(linear_algebra).
• Kernel_(algebra) wikiPageWikiLink Quotient_space_(topology).
• Kernel_(algebra) wikiPageWikiLink Rank-nullity_theorem.
• Kernel_(algebra) wikiPageWikiLink Rank_(linear_algebra).
• Kernel_(algebra) wikiPageWikiLink Rank_(matrix_theory).
• Kernel_(algebra) wikiPageWikiLink Rank–nullity_theorem.
• Kernel_(algebra) wikiPageWikiLink Real_line.
• Kernel_(algebra) wikiPageWikiLink Real_number.
• Kernel_(algebra) wikiPageWikiLink Regular_category.
• Kernel_(algebra) wikiPageWikiLink Ring_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Ring_homomorphism.
• Kernel_(algebra) wikiPageWikiLink Semigroup.
• Kernel_(algebra) wikiPageWikiLink Set_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Singleton_(mathematics).
• Kernel_(algebra) wikiPageWikiLink Singleton_set.
• Kernel_(algebra) wikiPageWikiLink Subalgebra.
• Kernel_(algebra) wikiPageWikiLink Subgroup.
• Kernel_(algebra) wikiPageWikiLink Submodule.
• Kernel_(algebra) wikiPageWikiLink Submonoid.
• Kernel_(algebra) wikiPageWikiLink Subring.
• Kernel_(algebra) wikiPageWikiLink Subset.
• Kernel_(algebra) wikiPageWikiLink Subtraction.

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