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A: The detailed solution is given below. Thank you
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A: In this question , we can solve the inequality .
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A: All we need to do is to find the points where the curve intersects the x axis.
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A: Topic:- algebra
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A: We can answer the question as per the graph in the following steps.
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A: The answer is - 1/e15
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- Prove that if a subring R of an integral domain D contains the unity element of D, then R is an integral domain. [Type here][Type here]Let R be a commutative ring with unity. Prove that deg(f(x)g(x))degf(x)+degg(x) for all nonzero f(x), g(x) in R[ x ], even if R in not an integral domain.18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is isomorphic to .
- [Type here] True or False Label each of the following statements as either true or false. 3. Every integral domain is a field. [Type here]If is a finite field with elements, and is a polynomial of positive degree over , find a formula for the number of elements in the ring .19. Find a specific example of two elements and in a ring such that and .
- [Type here] 23. Let be a Boolean ring with unity. Prove that every element ofexceptandis a zero divisor. [Type here][Type here] True or False Label each of the following statements as either true or false. 2. Every field is an integral domain. [Type here]22. Let be a ring with finite number of elements. Show that the characteristic of divides .