Let Zeven represent the set of even integers, {... -6, -4, -2, 0, 2, 4, 6, ...}. Determine if the system (Zeven, +): (i) is closed; (ii) is associative; (iii) has an identity element; (iv) has inverses; and (v) is commutative. Is (Zeven, +) a semi-group? Explain Is (Zeven, +) a group? Explain

Let Zeven represent the set of even integers, {... -6, -4, -2, 0, 2, 4, 6, ...}. Determine if the system (Zeven, +): (i) is closed; (ii) is associative; (iii) has an identity element; (iv) has inverses; and (v) is commutative. Is (Zeven, +) a semi-group? Explain Is (Zeven, +) a group? Explain

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 39E

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Question

Let Z^even represent the set of even integers, {... -6, -4, -2, 0, 2, 4, 6, ...}.

Determine if the system (Z^even, +): (i) is closed; (ii) is associative; (iii) has an identity element; (iv) has inverses; and (v) is commutative.

Is (Z^even, +) a semi-group? Explain

Is (Z^even, +) a group? Explain

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