 # Abstract algebra questions and answers

Recent questions in Abstract algebra 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 $$\displaystyle\epsilon^{{n}}={1}$$. We say that epsilon is primitive if every nth root of unity is $$\displaystyle\epsilon^{{k}}$$ for some k. Show that there are primitive nth roots of unity $$\displaystyle\epsilon_{{n}}\in\mathbb{C}$$ for all n, and find the degree of $$\displaystyle\mathbb{Q}\rightarrow\mathbb{Q}{\left(\epsilon_{{n}}\right)}$$ for $$\displaystyle{1}\le{n}\le{6}$$ rocedwrp 2020-11-10 Answered

### Find th eminimal polynomial of $$\displaystyle\sqrt{{2}}+\sqrt{{3}}$$ over $$\displaystyle\mathbb{Q}$$ Isa Trevino 2020-10-23 Answered

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

### Let $$\displaystyle{p},{q}\in\mathbb{Z}$$ be district primes. Prove that $$\displaystyle\mathbb{Q}{\left(\sqrt{{p}},\sqrt{{q}}\right)}=\mathbb{Q}{\left(\sqrt{{p}}+\sqrt{{q}}\right)}$$, and that $$\displaystyle\mathbb{Q}\subseteq\mathbb{Q}{\left(\sqrt{{p}}+\sqrt{{q}}\right)}$$ 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 at play. Don’t forget about the application of the Algebraic number theory studies as well.
...