Thank you.
Let Phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that if T is a subring of R, then the set W= {b S such that b = Phi(c) for some c T} is a subring of S. [Be specific of how and where you use that T is a subring of R.]
Solution
for this we only have to prove that
there exist identity
if b is in W then tere is a element -b in W such that
b - b = 0
so if phi(c) = b then phi(-c) = -b where c and -c are in T since T is a subring since phi is homeomorphism.
now if b and c are in W then there are d and f in T such that
phi ( d) =b and phi (f) = c
then phi (df) = phi(d) phi(f) = bc in W
so W is a ring and since it is subset of S so it is subring of S
.
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Thank you- Let Phi- R rightarrow S be a surjective homomorphism from t.docx
1. Thank you.
Let Phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that
if T is a subring of R, then the set W= {b S such that b = Phi(c) for some c T} is a subring of S.
[Be specific of how and where you use that T is a subring of R.]
Solution
for this we only have to prove that
there exist identity
if b is in W then tere is a element -b in W such that
b - b = 0
so if phi(c) = b then phi(-c) = -b where c and -c are in T since T is a subring since phi is
homeomorphism.
now if b and c are in W then there are d and f in T such that
2. phi ( d) =b and phi (f) = c
then phi (df) = phi(d) phi(f) = bc in W
so W is a ring and since it is subset of S so it is subring of S
![Thank you.
Let Phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that
if T is a subring of R, then the set W= {b S such that b = Phi(c) for some c T} is a subring of S.
[Be specific of how and where you use that T is a subring of R.]
Solution
for this we only have to prove that
there exist identity
if b is in W then tere is a element -b in W such that
b - b = 0
so if phi(c) = b then phi(-c) = -b where c and -c are in T since T is a subring since phi is
homeomorphism.
now if b and c are in W then there are d and f in T such that](https://image.slidesharecdn.com/thankyou-letphi-rrightarrowsbeasurjectivehomomorphismfromt-230202234605-1cdb7d4d/85/thank-you-let-phi-r-rightarrow-s-be-a-surjective-homomorphism-from-tdocx-1-320.jpg)
