p-adic integer

p-adic integer

[pē¦adik ′int·i·jər]
(mathematics)
For a fixed prime number p, a sequence of integers, x0, x1, …, such that xn -xn-1divisible by p n for all n ≥0; two such sequences, xn and yn , are considered equal if xn -yn is divisible by p n +1for all n ≥0, and the sum and product of two such sequences is defined by term-by-term addition and multiplication.
References in periodicals archive ?
For each integer b with 0 [less than or equal to] b [less than or equal to] p - 1 and each p-adic integer [alpha] [member of] [Z.
These modules play important roles in various areas of algebra, primarily commutative algebra, including rings of p-adic integers and certain power series rings over division rings.
p] be denoted by the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of [Q.