Compute the characteristic of the ring Z18 × Z15

Rivka Thorpe 2021-02-01 Answered

Compute the characteristic of the ring Z18×Z15

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bahaistag
Answered 2021-02-02 Author has 101 answers

Number of element in Z18×Z15 is 18×15=270.
So, 270x will be the zero element of Z18×Z15=(00)Z=(00) of for all xZ18×Z15. Let nn is charactiristic of Z18×Z15 then nn must divide 270 and again let (1,1)Z18×Z15(1,1)Z then n(1,1)=(n,n)(0,0)Z18×Z15Z, that is nn must be divisible by 18 and 15, infact nn must be least common multiple of 15 and 18. So, charactiristic of Z18×Z15=l.c.m(18,15)=90.

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