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# MTH721 - Commutative Algebra Assignment No. 01 Solution and Discussion Spring 2017 Due Date May 19, 2017

Question: 1                                                                                                                               Marks: 5

Let I, J and K are ideals in ring R. Show that .

Question: 2                                                                                                                               Marks: 5

Show that the binary operation * defined on  by  is a group.

Question: 3                                                                                                                               Marks: 5

Show that  defined by  for all is a ring homomorphism. Find . Determine whether it is an isomorphism or not? If it is not isomorphism than give reason.

Question: 4                                                                                                                               Marks: 5

Let I, J be an ideal in R. Show that if  then .

Question: 5                                                                                                                              Marks: 5

Question: 6                                                                                                                              Marks: 5

Consider the ideals . Calculate the minimal set of generators for ideals

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