I am looking for an abstract algebra book that covers groups, rings, and fields at an advanced level. I am coming from Baby Rudin and Axler's linear algebra book but have not taken any prior courses. I have heard Dummit and Foote, Fraleigh, and Herstein are the standard options but I know there are videos from Harvard and lecture notes from MIT corresponding to Artin's book and looking at the table of contents it seems very extensive. I have heard of Lang's undergraduate book but have not heard anything good nor bad about it so am not sure. I have also heard of Lang's and Hungerford's graduate books but am unsure if they would assume previous exposure? What have you either learned or taught from and what would y'all recommend.Thanks!
2026-04-03 04:19:40.1775189980
Looking for a abstract algebra book for at the advanced undergrad/early grad level that does not assume prior exposure
159 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in BOOK-RECOMMENDATION
- Books recommendations for a second lecture in functional analysis
- Book/Online Video Lectures/Notes Recommendation for Analysis(topics mentioned)
- Are there any analysis textbooks like Charles Pinter's A book of abstract algebra?
- Calculus book suggestion
- How to use the AOPS books?
- What are good books cover these topics?
- Book Recommendation: Introduction to probability theory (including stochastic processes)
- calculus of variations with double integral textbook?
- Probability that two random numbers have a Sørensen-Dice coefficient over a given threshold
- Algebraic geometry and algebraic topology used in string theory
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
I would definitely check out Aluffi's "Algebra : chapter 0", it's a good book, quite extensive, with pretty much no prerequisite. Lang's book called "Algebra" is probably just as extensive (in all fairness, Lang's book might even cover a bit more than Aluffi's), but in my opinion very unfriendly and hard to read, especially if it's your first approach. I can't say much about the other book you mention, I haven't used them as much or at all (except maybe Dummit & Foote, which is nice as well, but I'd still pick Aluffi over D&F).