Decide whether ZxZ = {(n,m) n,me Z} with addition and multiplication by components, give a ring structure. If not, then give the axiom that fails. If a ring is formed, state whether the ring is commutative, has unity, or is a field.

Decide whether ZxZ = {(n,m) n,me Z} with addition and multiplication by components, give a ring structure. If not, then give the axiom that fails. If a ring is formed, state whether the ring is commutative, has unity, or is a field.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 3E: Consider the set S={[0],[2],[4],[6],[8],[10],[12],[14],[16]}18, with addition and multiplication as...

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Question

MTH315
Tutorial Activity 12
Decide whether Z×Z = {(n,m)|n,m≤ Z} with addition and multiplication by components,
give a ring structure. If not, then give the axiom that fails. If a ring is formed, state whether
the ring is commutative, has unity, or is a field.

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