1
edit
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + − ==Other defintions== − Depending on the specific context, some elements of this definition may be somewhat different. For example, some authors include in the defintion that there exists a multiplicative identity.+ + + + + + + + + + + +
no edit summary
A '''ring''' in mathematics is a set of numbers closed under addition and multiplication where addition is [[commutative]], both operations are [[associative]], multiplication [[Distributive property|distributes]] over addition, there is an additive identity and additive inverses.
A '''ring''' in [[mathematics]] is a set ''R'' equipped with two [[binary]] [[operations]], usually called addition and multiplication, satisfying that
'''1.''' ''R'' with addition is a [[commutative]] [[group]];
'''2.''' ''R'' with multiplication is a [[semigroup]];
'''3.''' multiplication [[distributes]] over addition.
==Remarks==
A '''ring with unit''' is a ring for which multiplication has a [[neutral element]].
A '''division ring''' is a ring such that ''R'' with multiplication is a (not necessarily [[commutative]]) [[group]].