In number theory, the Hecke algebra corresponding to a congruence subgroup "Γ" of the modular group is spanned by elements of the double coset space formula_9; the algebra structure is that acquired from the multiplication of double cosets described above.

Also named for Kronecker are the Kronecker limit formula, Kronecker's congruence, Kronecker delta, Kronecker comb, Kronecker symbol, Kronecker product, Kronecker's method for factorizing polynomials, Kronecker substitution, Kronecker's theorem in number theory, and Kronecker's lemma.

In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem.

Quite simply, through what seems in retrospect to have been a fortuitous congruence of persons and events.

In the work Kepler discusses harmony and congruence in geometrical forms and physical phenomena.

It should be noted that when Kepler uses the term “harmony” it is not strictly referring to the musical definition, but rather, a broader definition encompassing congruence in Nature and the workings of both the celestial and terrestrial bodies.

Kepler divides "The Harmony of the World" into five long chapters: the first is on regular polygons; the second is on the congruence of figures; the third is on the origin of harmonic proportions in music; the fourth is on harmonic configurations in astrology; and the fifth on the harmony of the motions of the planets.

With respect to the timelike geodesic congruence of world lines obtained by integrating the timelike unit vector field formula_73, the "expansion tensor" shows that our test particles are expanding or contracting "isotropically" and "transversely to the direction of propagation".

A semigroup congruence formula_31 is an equivalence relation that is compatible with the semigroup operation.

Conversely, the kernel of any semigroup homomorphism is a semigroup congruence.

Congruence classes and factor monoids are the objects of study in string rewriting systems.

A nuclear congruence on "S" is one which is the kernel of an endomorphism of "S".