{[::] 1) 5. Assume that R a, b, c, d e Z and R' [a] (b) a, b, c, d e Z2 Given that %3D 0: R → R defined by 0 la] [이 is a homomorphism. Find kere. d

Q: 15. Verify the SSS Postulate for triangle congruence by using congruence transformations. Given: XY…

A: Given: XY¯≅RS¯,YZ¯≅ST¯,ZX¯≅TR¯ To prove: ∆XYZ≅∆RST

Q: 4. Let y: R→ S be a ring homomorphism. Prove that ': R[X] → S[X] given by soʻ (ao + a1X + ..a,X") =…

A:

Q: Which one(s) of the requirements of isomorphism does H : R" → Rª fail to satisfy? H((S1, S2, S3, S4,…

A:

Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

A:

Q: Prove that the following does not define an inner product R?: ((a, b), (c, d)) = ac – bd. on

A:

Q: The mapping : (Z6, +6) → (U4, X4) on my avong bas 0 is arounico at wey song has 18 uniton ai n3"…

A: Mapping :

Q: Exercise 7.24. (a) Suppose : Z36 → G is a surjective homomorphism, where |G| (b) (a) Suppose : Z25 →…

A: (a) Here we have given that ϕ:ℤ36→G is a surjective homomorphism, where G=12. Now, by the first…

Q: Problem 7 Let He Vam I tudom S = {(2,x) | x E I} CR², dT (81 Ing/ T= {(0,x) | x 1} CR², o ir aut

A:

Q: W 3. Lat R.S.T by rings and let w 4₁ iRDS and I₂ S&T boring. homomorphisms. Show that! V bu b)…

A:

Q: Question: Let Ø be R'. Let u be a a homomorphism of a with ring R unit in R. Show that Ø(u) is a…

A: Given that  ϕ be a ring homomorphism of a ring R onto a non-zero ring R' and u be the unit in R. To…