A remark on the notation : Because it is common to consider several congruence relations for different moduli at the same time, the modulus is incorporated in the notation.
12.
In abstract algebra, congruence relations on the underlying set of an algebra allow the algebra to induce an algebra on the equivalence classes of the relation, called a quotient algebra.
13.
From the point of view of abstract algebra, congruence modulo n is a congruence relation on the ring of integers, and arithmetic modulo n occurs on the corresponding quotient ring.
14.
For values of " n " satisfying certain congruence relations, one can find an expansion for 4 / " n " automatically as an instance of a polynomial identity.
15.
The following year, on 16 March 1883, he delivered a short account of his congruence relation ( Zeller's congruence ), which was published in the society's journal.
16.
Both \ sim _ e and \ sim _ l suffer from the problem that they are not " congruence relations " in the sense that they are not preserved by all process constructs.
17.
The prototypical theorem, the Eichler Shimura congruence relation, implies that the Hasse Weil zeta function of a modular curve is a product of L-functions associated to explicitly determined modular forms of weight 2.
18.
One may remedy this problem by considering the maximal congruence relations included in \ sim _ e and \ sim _ l, known as " early congruence " and " late congruence ", respectively.
19.
In universal algebra, an abstract algebra " A " is called " simple " if and only if it has no nontrivial congruence relations, or equivalently, if every homomorphism with domain " A " is either injective or constant.
20.
In abstract algebra, a "'congruence relation "'( or simply "'congruence "') is an equivalence relation on an algebraic structure ( such as a ring, or vector space ) that is compatible with the structure.
