Consider the ring Z/5Z = {0, 1,2,3,4} (a) Fill in the addition and multiplication tables for this ring: 0 1 2 3 4 + 0 I Z 3 x0I2|3|4 0 I 2 3 (b) Show that each non-zero a € Z/5Z is a unit, and determine its multiplicative inverse a−¹. Hint: Use your multiplication table from part (a). (c) Explain why Z/5Z is a field.

Q: Determine if indicated set forms a ring: S = {ri | r E R, i2 = -1} under the operations on complex…

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Q: 2. Find all values of p such that Z„[r]/{x² + 1) is a field.

A: We know that results

Q: 10. Decompose x* + 4.x² + 1 into a product of irreducible polynomials in the following rings: (a)…

A: To find - Decompose x4 + 4x2 + 1 into a product of irreducible polynomials in the following rings :…

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Q: Consider the quotient ring R = Q[x] x² − 4 > (a) Give an example of a zero divisor in R. Explain why…

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Q: a) Factor a + r³ + x into irreducible polynomials in Z2[x];

A: We shall solve first Que only, if you want others to be solved kindly post it again by mentioning…