Definition:Integers Modulo m

Definition

Let $m \in \Z$ be an integer.

The integers modulo $m$ are the set of least positive residues of the set of residue classes modulo $m$:

$\Z_m = \set {0, 1, \ldots, m - 1}$

Also see

• Definition:Congruence Modulo Integer

• Definition:Modulo Addition
• Definition:Modulo Multiplication

• Definition:Set of Residue Classes

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields: Example $4$
• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.5$. Congruence of integers
• 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation
• 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): $\S 1$: Some examples of groups
• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $2$
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Equivalence Relations: $\S 18$
• 1974: Thomas W. Hungerford: Algebra ... (previous) ... (next): $\text{I}$: Groups: $\S 1$: Semigroups, Monoids and Groups
• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Appendix $\text{A}.3$: Equivalence Relations
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 18$: Congruence classes
• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 2.3$: Congruences
• 1988: Dominic Welsh: Codes and Cryptography ... (previous) ... (next): Notation