In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.* List the positive integers that are divisors of 20 . *An integer d is a divisor of an integer n (and n is a multiple of d ) if n = k d for some integer for some integer k . An integer n is even if 2 is a divisor of n ; otherwise, n is odd. An integer p > 1 is prime if its only positive divisors are 1 and p .
In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.* List the positive integers that are divisors of 20 . *An integer d is a divisor of an integer n (and n is a multiple of d ) if n = k d for some integer for some integer k . An integer n is even if 2 is a divisor of n ; otherwise, n is odd. An integer p > 1 is prime if its only positive divisors are 1 and p .
Solution Summary: The author explains that the list of positive integers that are divisors of 20 is left1,2,4,5,10,20right
In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.*
List the positive integers that are divisors of
20
.
*An integer
d
is a divisor of an integer
n
(and
n
is a multiple of
d
) if
n
=
k
d
for some integer for some integer
k
. An integer
n
is even if
2
is a divisor of
n
; otherwise,
n
is odd. An integer
p
>
1
is prime if its only positive divisors are
1
and
p
.
these are solutions to a tutorial that was done and im a little lost. can someone please explain to me how these iterations function, for example i Do not know how each set of matrices produces a number if someine could explain how its done and provide steps it would be greatly appreciated thanks.
Q1) Classify the following statements as a true or false statements
a. Any ring with identity is a finitely generated right R module.-
b. An ideal 22 is small ideal in Z
c. A nontrivial direct summand of a module cannot be large or small submodule
d. The sum of a finite family of small submodules of a module M is small in M
A module M 0 is called directly indecomposable if and only if 0 and M are
the only direct summands of M
f. A monomorphism a: M-N is said to split if and only if Ker(a) is a direct-
summand in M
& Z₂ contains no minimal submodules
h. Qz is a finitely generated module
i. Every divisible Z-module is injective
j. Every free module is a projective module
Q4) Give an example and explain your claim in each case
a) A module M which has two composition senes 7
b) A free subset of a modale
c) A free module
24
d) A module contains a direct summand submodule 7,
e) A short exact sequence of modules 74.
*************
*********************************
Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
Chapter 7 Solutions
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY