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Integers in the same congruence class a ≡ b (mod n ... and is equal to it if and only if the group is cyclic. Subgroup of false witnesses ... C 18: 18: 18: 2 51 C 2 ...
An abstract group defined by this multiplication is often denoted C n, and we say that G is isomorphic to the standard cyclic group C n. Such a group is also isomorphic to Z/nZ, the group of integers modulo n with the addition operation, which is the standard cyclic group in additive notation.
For example, += and -= are often called plus equal(s) and minus equal(s), instead of the more verbose "assignment by addition" and "assignment by subtraction". The binding of operators in C and C++ is specified (in the corresponding Standards) by a factored language grammar, rather than a precedence table. This creates some subtle conflicts.
The equivalence class modulo m of an integer a is the set of all integers of the form a + k m, where k is any integer. It is called the congruence class or residue class of a modulo m, and may be denoted as (a mod m), or as a or [a] when the modulus m is known from the context.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
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Multiplication in a finite field is multiplication modulo an irreducible reducing polynomial used to define the finite field. (I.e., it is multiplication followed by division using the reducing polynomial as the divisor—the remainder is the product.) The symbol "•" may be used to denote multiplication in a finite field.
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