True/False a. Zz x71 has characteristic zero. b. The direct product of two field

Question

True/False a. Zz x71 has characteristic zero. b. The direct product of two fields is an integral domain. C. Every abelian group is cyclic. d. A cyclic group can have at most one generator. e. When a group is partitioned into left cosets of one of its subgroups, each cell of the partition has the same number of elements. f 7x is a unit in Q [x]. g. If G is an abelian group and H s G, then H G and the group G/H is abelian. h. If G is a finite group and n 2 1 is an integer that divides the order of G. then there is an element of g e G such that the order of g is n. -i. Every element in a ring has an additive inverse. j. Every element in a division ring has a multiplicative inverse.

Explanation / Answer

a - true

b - true

c - false

d - true

e - false

f - false

g - false

h - true

i - true

j - false

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