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###### Vijay posted an Question
June 29, 2022 • 20:32 pm 30 points
• CSIR NET
• Mathematical Sciences

## Example : let r be a commutative ring and r[x] be the polynomial ring in one variable over r. (a) ifr is a ufd, then r[x] is a ufd (b) if r is a pid, then r[x]

Example : Let R be a commutative ring and R[x] be the polynomial ring in one variable over R. (A) IfR is a UFD, then R[X] is a UFD (B) If R is a PID, then R[x] is a PID C) If R is an Eucliden domain, then R[a] is an Euclidean domain (D) If R is a field, then RX] is an Euclidean domain

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