Question: Only question (b) please! All the given information is in the image (1) Let G = {e, g,g?} = (g) be the group of order

Only question (b) please! All the given information is in the image

(1) Let G = {e, g,g?} = (g) be the group of order 3, and consider the ring R = {ae + bg + cg2 | a, b, ce @} where (ajet big + cig?) + (age + bag + cag?) = (a1 + a2)e + (b1 + b2)g + (c1 + c2)g" and (ale + big + cig?)(age + bag + cag?) = (ala2 + bic2 + c1b2)e + (a1b2 + bla2 + cic2)g + (alc2 + bib2 + cla2)g2 (a) Show that & : R - Q given by E( ac + bg + cg? ) = atb+ c is a homomorphism. (b) Show that Ker(e) = (g -e), i.e. 1g - le

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