There are two ways of forming quotients of quantale-like structures: using nuclei or congruences
Furthermore operations on two good congruences
give good congruences
I thus assume that overall congruence
is a linear combination of issue specific congruences
and that the factor loadings for each issue are the coefficients of this linear combination.
We also describe connections between ideals and congruences
n-1]) the last three congruences
of (4) hold and we get case III) of Proposition 4.
If A is an ideal of KU-algebra G, then the relation ~ is a congruence
These three patterns are called Ramanujan's partition congruences
An American scholar of mysticism, Spector says it was the only detailed demonstration of the congruences
between the New Testament and an adapted form of Lurianic Kabbalism, and created the foundation for virtually every version of Christian Kabbalism since the 17th century.
Recently, q-analogs of classical congruences
have been studied by several authors including (Cla95), (And99), (SP07), (Pan07), (CP08), (Dil08).
K]) from the set of all congruences
on S onto the set of all congruence
pairs on S, where [[sigma].
In a clever and logical system that builds from previous knowledge, this covers such core topics as divisibility and primes, congruences
, cryptography, and quadratic residues, then addresses arithmetic functions, large primes, continued fractions, and diophantine equations, closing with advanced topics such as analytic number theory, elliptic curves, and the relationship between logic and number theory.
Nothing in the definition of partitions hinted that such relationships, called congruences
, should exist or that the prime numbers 5, 7, and 11 should play a special role.
of Illinois-Springfield) walks fellow mathematicians through are Jacobi's triple product identity, the Rogers-Ramanujan identities, the "most beautiful identity," and Ramanujan's congruences
Shards were used to give a geometric description of lattice congruences
of the weak order.
Doberkat develops the theory of stochastic relations as a foundation for Markov transition systems, investigating such central ideas as congruences
and morphisms and applying them to monoidal structure.