Unformatted text preview: polynomial f ( x ) which generates the principal ideal I ∩ Q [ x ] in Q [ x ]. (7) Prove or disprove: If H 1 and H 2 are subgroups of a ﬁnite group G then their product H 1 · H 2 is a subgroup of G . (8) Prove or disprove: If I is an ideal in a principal ideal domain R then every ideal in the quotient ring R/I is principal. (9) Prove or disprove: There exists a term ordering such that the subset { x 3 + y 2 ,x 2 + y } of Q [ x,y ] is a Gr¨obner basis. (10) Prove or disprove: If R is the quotient ring Q [ x,y, z ] / h x · zy 2 i then every irreducible element in R is prime....
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This note was uploaded on 02/03/2011 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at Berkeley.
 Spring '08
 OGUS
 Math, Algebra

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