Integer (computer science) at least 32 bits on any computer. Programmers may also incorrectly assume that a pointer can be converted to an integer without loss of information, which may work on (some) 32-bit computers, but fail on 64-bit computers with 64-bit pointers and 32-bit integers. A "short integer" can represent a whole number that may take less storage, while having a smaller range, compared with a standard integer on the same machine. In C, it is denoted by short. It is required to be at least 16 bits, and is often smaller than a standard integer, but this is not required. A
Algebraic integer . Each algebraic integer belongs to the ring of integers of some number field. A number is an algebraic integer if and only if the ring is finitely generated as an Abelian group, which is to say, as a -module. The following are equivalent definitions of an algebraic integer. Let be a number field (i.e., a finite extension of , the set of rational numbers), in other words, for some algebraic number by the primitive element theorem. Algebraic integers are a special case of integral elements of a ring extension. In particular, an algebraic integer is an integral element of