3- For any R-module ,let M [x]denote the set of all polynomials in x with coefficient in M, that is to say expression of the form m.+mix+...+m,x.(mi eM). Defining the product of an element of R[x] and an element of M[x] in the obvious way, show that M[x] is an R[x]-module. Show that M[x] = R[x] ®R M.
3- For any R-module ,let M [x]denote the set of all polynomials in x with coefficient in M, that is to say expression of the form m.+mix+...+m,x.(mi eM). Defining the product of an element of R[x] and an element of M[x] in the obvious way, show that M[x] is an R[x]-module. Show that M[x] = R[x] ®R M.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 23E: [Type here]
23. Let be a Boolean ring with unity. Prove that every element ofexceptandis a zero...
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