“residue class”的概念、定义、习题解题方法及翻译-数学辞典

单词

residue class

释义

residue class

(modulo n) An equivalence class for the equivalence relation of congruence modulo n. So, two integers are in the same class if they have the same remainder upon division by n. If [a] denotes the residue class modulo n containing a, the residue classes modulo n can be represented as [0], [1], [2],…, [n−1]. The sum and product of residue classes are defined by

where it is necessary to show these definitions are well defined and independent of the choice of representatives a and b. With this addition and multiplication, the set, denoted by ℤn, of residue classes modulo n forms a commutative ring with identity. If n is composite, the ring ℤn has zero-divisors, but when p is prime ℤp is a field.

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。