kernel congruence

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• Kernel (algebra) — 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 matrix, also… …   Wikipedia

• Congruence subgroup — In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example would be invertible 2x2 integer matrices of determinant 1, such that the off… …   Wikipedia

• Congruence relation — See congruence (geometry) for the term as used in elementary geometry. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is… …   Wikipedia

• Kernel (set theory) — In mathematics, the kernel of a function f may be taken to be either*the equivalence relation on the function s domain that roughly expresses the idea of equivalent as far as the function f can tell , or *the corresponding partition of the domain …   Wikipedia

• Equivalence relation — In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… …   Wikipedia

• Isomorphism theorem — In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules,… …   Wikipedia

• Modular group — For a group whose lattice of subgroups is modular see Iwasawa group. In mathematics, the modular group Γ is a fundamental object of study in number theory, geometry, algebra, and many other areas of advanced mathematics. The modular group can be… …   Wikipedia

• Ideal (ring theory) — In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept allows the generalization in an appropriate way of some important properties of integers like even number or multiple of 3 . For instance, in… …   Wikipedia

• Orthogonal group — Group theory Group theory …   Wikipedia

• Quotient algebra — In mathematics, a quotient algebra, (where algebra is used in the sense of universal algebra), also called a factor algebra is obtained by partitioning the elements of an algebra in equivalence classes given by a congruence, that is an… …   Wikipedia

• Semigroup — This article is about the algebraic structure. For applications to differential equations, see C0 semigroup. In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup… …   Wikipedia