# Oldest abstract algebra book with exercises?

Per the title, what are some of the oldest abstract algebra books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am already aware of the books of Dickson and van der Waerden.

For a pre-20th century textbook: Modern Higher Algebra by George Salmon (1876) has exercises (with solutions).

If I may broaden the query from "abstract algebra" to more general "algebra", I note that Elements of Algebra by Euler (1770) has more than one hundred exercises. The exercises are discussed in The origin of the problems in Euler’s algebra.

Here is an example, from the chapter on cubic equations [source].

And another example (find an integer $$x$$ such that $$2x^2-5$$ is a cube) [source]

Answered by Carlo Beenakker on November 9, 2021

Two important early 20th-century abstract algebra textbooks that were superseded by van der Waerden are:

Hasse, H., 1926. Höhre Algebra.

Haupt, O., 1929, Einführung In Die Algebra, Zweiter Band - Mit Einem Anhang Von W. Krull, Akademische Verlagsgesellschaft M. B. H., Leipzig.

For an in-depth historical account of the transition from algebra to abstract algebra (including discussions of the various textbooks) see:

Leo Corry, 1996, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser Verlag.

Answered by Philip Ehrlich on November 9, 2021

I think the following references might be useful:

H. Weber (1895/1896): Lehrbuch der Algebra, 2 volumes. Vieweg, Braunschweig. It includes examples, but it does not have any separate exercises.

E. Artin (1938): Foundations of Galois Theory. New York University Lecture Notes, New York.

N. Bourbaki (1947): Éléments de Mathématique, Algèbre. Hermann, Paris.

I am not totally sure whether the last two references include exercises.

Answered by MaryS. on November 9, 2021

## Related Questions

### Sparse perturbation

0  Asked on December 1, 2020 by yiming-xu

### What is known about the “unitary group” of a rigged Hilbert space?

2  Asked on November 30, 2020

### Odd Steinhaus problem for finite sets

0  Asked on November 30, 2020 by domotorp

### Higher-order derivatives of $(e^x + e^{-x})^{-1}$

1  Asked on November 28, 2020 by tobias

### Smallness condition for augmented algebras

1  Asked on November 28, 2020 by ttip

### number of integer points inside a triangle and its area

1  Asked on November 27, 2020 by johnny-t

### Unitary orbits on the Grassmann manifold of 2-planes in complex affine space

1  Asked on November 26, 2020 by norman-goldstein

### Should the formula for the inverse of a 2×2 matrix be obvious?

9  Asked on November 21, 2020 by frank-thorne

### Hodge structure and rational coefficients

0  Asked on November 19, 2020 by dmitry-vaintrob

### Optimal path with multiple costs

2  Asked on November 18, 2020 by lchen

### Can a fixed finite-length straightedge and finite-size compass still construct all constructible points in the plane?

2  Asked on November 17, 2020 by joel-david-hamkins

### Genus $0$ algebraic curves integral points decidable?

0  Asked on November 14, 2020 by 1

### Interlocking (weak) factorization systems

0  Asked on November 9, 2020 by tim-campion

### Monte Carlo simulations

3  Asked on November 7, 2020 by alekk

### Measurable total order

1  Asked on November 5, 2020 by aryeh-kontorovich

### Recover approximate monotonicity of induced norms

1  Asked on November 3, 2020 by ippiki-ookami

### Geodesics and potential function

0  Asked on October 29, 2020 by bruno-peixoto

### Independent increments for the Brownian motion on a Riemannian manifold

0  Asked on October 26, 2020 by alex-m

### Multivariate monotonic function

2  Asked on October 25, 2020 by kurisuto-asutora