11. Determine if the following mappings are ring homomorphisms: (a) f:Q→Q defined by f(x) = |x| for all x e Q. b' a (b) g : C → M2(R) defined by g(a+bi) = - b a (c) h: Z[ V2]¬Z[ V2] defined by h(a + b /2) = a - b2.
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Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
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help no.11
![11. Determine if the following mappings are ring homomorphisms:
(a) f:Q→Q defined by f(x) = |x| for all x e Q.
a
b'
(b) g : C → M2(R) defined by g(a+bi) =
a
a - b/2.
(c) h: Z[/2]¬Z[ V2] defined by h(a + b v2) = a - t
12. Let f: R → S be a ring homomorphism. Prove that
(a) Ker(f) is a subring of R.
(b) If K is a subring of R, then f(K) is a subring of S.
(c) F is one-to-one if and only if Ker(f) = {0r}.
13. Show that T = {a+
b/3] a,be Z} is a subring of R.
14. Let R be a ring, a e R andI={sa|s e R}
(a) Show that ri e I for all r eR and i el.
(b) Show that I is a subring ofR.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bc36662-e81e-4805-a9ba-e756ced76ed7%2Fdc964826-ede2-40df-bb5a-dd33f1b719d7%2Fpgdd3vc_processed.png&w=3840&q=75)
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