Download OU B.Sc 2019 June-July 4th Semester 3121 Mathematics Question Paper

Download OU (Osmania University) BSc (Bachelor of Science - Maths, Electronics, Statistics, Computer Science, Biochemistry, Chemistry & Biotechnology) 2019 June-July 2nd Year 2nd Semester (4th Semester) (2-2) 3121 Mathematics Previous Question Paper

Le: Gbeagmupandeeia nonempty
,lfabsHVaJeHanda' eHVae
'2; mlagvmh real coef?cients and let A denote
? w arm 0 then prove that'A is an ideal of R
'iin
n.?
gRtoa?ngS?wenKer?=keR/9(r)=0)
7 ? Let ? be a rihg homom .
is an ideal of R.
8 If 0? IS an integ dor?in then - :2 D[x] is an integral domain.
? = 60 Marks)
;, _er Type)
_m the questions.
1c more over if l< a>l=n then the order of
? and for each positive divisor k of n, 916
oforderKnamely< a > .
. 'i
Note: Answ
9 (a) Every subgroup of a cyclic g r '
' any subgroup of < a> is a di ':-
group < a > has exactly one sm -
:?ar
.(b') De'?ngAltemgting gr-o?upqu ? so prove that A.1 has order 31?, if n > 1,
:50 (a) Prove that the group of rota . ~ b? Is isomorphic to S4.
(b) Let G be a groUp and is! ? of G. If 700) is cyclic then G is '
abelian.
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? > , 11 (a) Prove thai 2,1 I 1 21.11: I agb?j;
< (b) Lat_'_R be 'a oommuta?yp?g,
? ' Integral amm Handed?! ,,
1.
'2 (a) n R u; 5 WWW?
contains a subn'ng isomp -
a subdng lsomorphlc to Z.
. . I! '
. (b)Let,Sa= [f], a) ./
5 V' mama.
?de ?3 n >032?!)er R W?
" ._ I! me'charactodwc
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