Mathematical Science Algebra Rings & Ideals

For two indeterminates x, y, let R =Ā š”½3[x] and S = R[y].Ā Which of the following statements are true?Ā 

1
S is a principal ideal domainĀ 
2
S/(y2Ā + x2)Ā is a unique factorization domainĀ 
3
S is a unique factorization domainĀ 
4
S/(x)Ā is a principal ideal domainĀ 

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