Prove that L = {a + b √ 5i | a, b ∈ Q} is a...

Prove that L = {a + b √ 5i | a, b ∈ Q} is a field containing the roots of x² + 5. Moreover, prove that if Q ⊆ K ⊆ C is a field containing the roots of x² + 5, then L ⊆ K.

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Colby Messinger answered 2 years ago

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L...

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L = { aib2i : i > 0} 2) Prove the language M is not regular, over the alphabet Σ = {a, b}. M = { wwR : w is an element of Σ* i.e. w is any string, and wR means the string w written in reverse}. In other words, language M is even-length palindromes.

Answer correctly supporting with clear explanation. Classify the set Q( √ 5i) as a ring or...

Answer correctly supporting with clear explanation. Classify the set Q( √ 5i) as a ring or a field. To justify your answer, show that the set satisfies the axioms for ring or field.

Let A = {a+b*sqrt14: a,b∈Z}. Prove that A ∩ Q = Z. Explain is set A...

Let A = {a+b*sqrt14: a,b∈Z}. Prove that A ∩ Q = Z. Explain is set A countable?

(a) Prove that Q(sqareroot 5)={a+b sqareroot 5 ; a,b in Z} is a subring of Z....

(a) Prove that Q(sqareroot 5)={a+b sqareroot 5 ; a,b in Z} is a subring of Z. (b) Show that Q(sqareroot 5) is a conmutative ring. (c) Show that Q(sqareroot 5) has a multiplicative identity. (d) show that Q(sqareroot 5) is a field.(Hint : you want to mulitply something by he conjugate.) (Abstract Algebra)

prove that L^∞ is complete

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Prove that L = {a + b √ 5i | a, b ∈ Q} is a...

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