4. Consider P = P(3, V15) = {a + b/15|a, be Z, 3|a} and Z[V15] = {a + bv15|a, b e Z}. (a) Prove that P is an ideal of the ring Z[V15). (b) Determine the quotient ring Z[V15]/P. (c) Construct the addition and multiplication tables for the quotient ring Z[V15]/P.

4. Consider P = P(3, V15) = {a + b/15|a, be Z, 3|a} and Z[V15] = {a + bv15|a, b e Z}. (a) Prove that P is an ideal of the ring Z[V15). (b) Determine the quotient ring Z[V15]/P. (c) Construct the addition and multiplication tables for the quotient ring Z[V15]/P.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

4. Consider P = P(3, v15) = {a + bv15|a, b e Z, 3|a} and Z[V15] = {a + byV15|a, b e Z}.
(a) Prove that P is an ideal of the ring Z[V15).
(b) Determine the quotient ring Z[V15]/P.
(c) Construct the addition and multiplication tables for the quotient ring Z[V15]/P.

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