5. Tim cac udc oda khOng trong vanh Z/6Z.
6. Chang minh Z/nZ (it x 0) la mat mien nguyen khi va chi khi n la nguyen td. chi khi n la nguyen td.
7. Chang minh tap hop X = Z x Z ding vdi hai phep toan (a t, b i ) + (a2 , 6 2 ) = (a 1 + a2, b i + b2) (a t, b i ) + (a2 , 6 2 ) = (a 1 + a2, b i + b2)
b 1 )(a 2, b 2) = (a t at , b 16 2 )
la mat vanh giao hoan, c6 don id.. Hay Um tat ca the vac dm khOng vanh nay. khOng vanh nay.
8. Gilt au X la mat vanh ea tinh chat sau day :
x 2 = xvdi mm x E X.
Cluing minh rang
a) x = -x yea mai x E X.
b) X la vanh giao ham.
c) Neu. X la vanh kh6ng cd tnic dm 0, cd nhieu hon met phan thi X la mien nguyen. phan thi X la mien nguyen.
9. Clic vanh b Mc bid tap 1), 2), 3) la tug vanh con cha nhirng vanh nao ? nhirng vanh nao ?
10. Cho X lit met vanh thy j, A vb. B la hai idean elk X Chung minh rang be phan Chung minh rang be phan
A +B= {a+b I aEA,bE B} la met idean dm X. la met idean dm X.
11. Cho X la met vanh thy y, n la mat s6 nguyen cho tru0e. Chang minh be phan Chang minh be phan
A=IxEXI nx = 01 la met idean cha X. la met idean cha X.
12. Cho X la mat vanh thy j, a e X. Chung minh rang 136 phan
oX=faxIxEX1
la met idean phai cha X, va be phan
Xa = {xaIxEX}
la mat idean trai cha X.
13. GM sit X la met mien nguyen va n la cap (oh II, § 2, 2, dinh nghia 5) dm phan iv don vi e. Chung minh 2, dinh nghia 5) dm phan iv don vi e. Chung minh
a) n la met s6 nguyen te,
b) Mei phtin tv khac khang x e X cd cap n. c) Be phan c) Be phan
mX = { mx I x E X},
vbi m la met se nguyen cho trite; la mat idean dm X.
d) X/mX = X nen in la b6i eta it,
14. Gig. sit X le mot vanh giao hoan, th don vi. MOt idean A m X dm X g9i la Wean t6i dui va chi nth the idean A m X dm X g9i la Wean t6i dui va chi nth the idean caa X elute A chinh la X va ban than A. Mot idean P # X mia