What is Abstract algebra: Definition and 457 Discussions
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra.
Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures.
Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called variety of groups.
I was given this problem to work out but I'm still a little bad when it comes to proofs, but here's the question. I have given it a little thought but I can't seem to prove what I feel is the correct answer without brute forcing the answer in such an ugly way.
Let G = S_7, where S_7 is the...
This should probably be posted in the math forums but I guess it would fall under here because it's a HW question due late tomorrow.
If G is a group, prove that Aut(G) and Inn(G) are groups, where Aut(G) is the set of automorphisms of G and Inn(G) is the set of inner automorphisms of G
For...
Hello,
I am a student at CMU, enrolled in the Abstract Algebra class.
I'm having trouble with a few problems, see if you can figure them out.
Show that for every subgroup $J$ of $S_n|n\geq 2$, where $S$ is the symmetric group, either all or exactly half of the permutations in $J$ are...
I'm having trouble finding any good books and sites from which i can learn abstract algebra. Does anyone have any good suggestions so that i can learn the course? please include prices if possible
My question is regarding abstract algebra.
Suppost that B is a 10-cycle.
For which integers i between 2 and 10 is
B^(i) also a 10-cycle?
I know that the answer is 3, 7, and 9 I just don't know
how you arrive at these numbers. If...
Frustrating step in a proof -- basic abstract algebra
Hello all, I am trying to work on a proof related to information theory, and I have gotten stuck. I am nearly 100% this is true, but it might not be . . . and I am having trouble coming up with a proo for it in any case!
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M...
I downloaded that book from the physics Napster. It looks like something I should be able to handle, but I need help understanding some of the notation.
"Any set called an index set is assumed to be non-void. Suppose T is an index set and for each t within T, At is a set.
[inter] At =...