 # Abstract algebra questions and answers

Recent questions in Abstract algebra foass77W 2021-01-08 Answered

### Find the inverse of $x+1\in \mathbb{Q}\frac{x}{{x}^{3}-2}$. Explain why this is the same as finding the inverse of $\sqrt{2}\in \mathbb{R}$. Lewis Harvey 2021-01-06 Answered

### Prove that a group of even order must have an element of order 2. Joni Kenny 2021-01-05 Answered

### Let a,b be coprime integers. Prove that every integer $x>ab-a-b$ can be written as $na+mb$ where n,m are non negative integers. Prove that $ab-a-b$ cannot be expressed in this form. Dolly Robinson 2021-01-04 Answered

### Let F be a field and consider the ring of polynominals in two variables over F,F[x,y]. Prove that the functions sending a polyomial f(x,y) to its degree in x, its degree in y, and its total degree (i.e, the highest $i+j$ where ${x}^{i}{y}^{i}$ appears with a nonzero coefficient) all fail o be norm making F[x,y] a Euclidean domain. texelaare 2020-12-30 Answered

### In the froup ${Z}_{12}$, find $|a|,|b|$, and $|a+b|$ $a=3,b=8$ hexacordoK 2020-12-27 Answered

### Use Principle of MI to verify (i) If $n\in \mathbb{Z}$ is a positive ineger then ${2}^{n}{3}^{xn}-1$ divisible by 17. (ii) For all positive integers $n\ge 5$, ${2}^{k}>{k}^{2}$ Rui Baldwin 2020-12-15 Answered

### Let F be i field with subfields K,L. Prove that there is a largest subfield of F contained in both K and L, and a smallest subfield of containung both K and L. nicekikah 2020-12-15 Answered

### How many subgroups of order 4 does ${D}_{4}$ have? Harlen Pritchard 2020-12-15 Answered

### Suppose G is a group, H a subgroup of G, and a and b elements of G. If $a\in bH$ then $b\in aH$. iohanetc 2020-11-29 Answered

### How to find the value of U(n) on abstract algebra Example U(8) = {1,3,5,7} Khadija Wells 2020-11-20 Answered

### Prove that in any group, an element and its inverse have the same order. mattgondek4 2020-11-11 Answered

### An nth root of unity epsilon is an element such that ${ϵ}^{n}=1$. We say that epsilon is primitive if every nth root of unity is ${ϵ}^{k}$ for some k. Show that there are primitive nth roots of unity ${ϵ}_{n}\in \mathbb{C}$ for all n, and find the degree of $\mathbb{Q}\to \mathbb{Q}\left({ϵ}_{n}\right)$ for $1\le n\le 6$ rocedwrp 2020-11-10 Answered

### Find th eminimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb{Q}$ Mylo O'Moore 2020-10-23 Answered

### Write down a definition of a subfield. Prove that the intersection of a set of subfields of a field F is again a field Isa Trevino 2020-10-23 Answered

### Let F be a field. Prove that there are infinitely many irreducible monic polynomials naivlingr 2020-10-20 Answered

### Let $p,q\in \mathbb{Z}$ be district primes. Prove that $\mathbb{Q}\left(\sqrt{p},\sqrt{q}\right)=\mathbb{Q}\left(\sqrt{p}+\sqrt{q}\right)$, and that $\mathbb{Q}\subseteq \mathbb{Q}\left(\sqrt{p}+\sqrt{q}\right)$ is a degree 4 extension.

Coming up with good abstract algebra examples is essential for those who are trying to come up with the answers to theoretical questions both in Engineering and Data Science disciplines. The college students will be able to discover abstract algebra questions and answers provided by our friendly experts that will help you to understand abstract algebra questions with various examples based on high-energy physics, cryptography, and the number theory. Remember that the trick is to use number sequences to generalize the set of various integers and transformations of functions equation problems at play. Don’t forget about the application of the Algebraic number theory studies as well.