Let A be a cyclic R module of order r R (a) If s R is relatively prime to r, then sA A and A s 0 (b) If s divides r, say sk r, then sA R (k) and A s R (s) ...

ANSWER a If s R is relatively prime to r then s has a multiplicative inverse modulo r say s1 Then for any a A we have sa s1a s1a s1a s times s1 r t1a ...

Let A be a cyclic R-module of order r R. (a) If s R is

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Let A be a cyclic R-module of order r ϵ R.

(a) If s ϵ R is relatively prime to r, then sA = A and A[s] = 0.

(b) If s divides r, say sk = r, then sA ≅ R/(k) and A[s] ≅ R/(s).

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:04 AM

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Let A be a cyclic R-module of order r R. (a) If s R is

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ANSWER a If s R is relatively prime to r then s has a multiplicative inverse modulo r say s1 Then for any a A we have sa s1a s1a s1a s times s1 r t1a ...View the full answer

Algebra Graduate Texts In Mathematics 73

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