Question

anyone knw wts the field and ring in group theory?

Answer 1

Fields are sets which obey the field axioms. A ring is almost the same, except that it doesn't have division so no multiplicative inverses.

Answer 2

So the set of real numbers are a field, the set of rational numbers are a field, the set of integers is a ring, etc.

Answer 3

ahaa ok i think i gt the idea with this example thx :)

Answer 4

Rings, fields and groups are all different types of algebraic objects. Groups are the most 'simple' in as much as they are a set with one binary operator; rings and fields have two binary operators ('addition' and 'multiplication')

Every field is a ring, as described above, and every ring is a group under the 'addition' operating of the ring.

But nearly all important groups that are studied as groups are not and cannot be made into rings or fields.

Answer 5

thank james :)

Answer 6

Thanks so much for this!!!