Open Questions: Algebra
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See also: Symmetry --
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The word problem
Algebraic K-theory
Commutative algebra
Inverse Galois theory
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Site indexes
-
Math Forum Internet Mathematics Library: Modern Algebra
- Alphabetized list of links with extensive annotations.
-
The Math Forum: Modern Algebra
- Selected list of links with extensive annotations.
-
Mathematics Archives - Abstract Algebra
- Extensive annotated list of links.
-
Open Directory Project: Algebra
- Categorized and annotated algebra links. A version of this
list is at
Google, with entries sorted in "page rank" order.
-
Galaxy: Algebra
- Categorized site directory. Entries usually include
descriptive annotations.
There are also indexes for
group theory,
(more
here),
ring theory,
field theory, and
linear algebra
(more
here).
Sites with general resources
-
Abstract Algebra Online
- Contains a list of many links organized by topic, a glossary
of algebra terms, and an index of important theorems.
Site is maintained by John Beachy and is based on his abstract
algebtra textbooks.
Surveys, overviews, tutorials
-
Abstract algebra
- Article from
Wikipedia.
-
Wikibooks: Abstract Algebra
- Textbook in the
Wikibooks collection. A work in progress, but already contains
much useful information.
Topics covered include:
Groups,
Rings,
Category theory,
Finite fields.
-
Abstract algebra
- Elementary introduction to abstract algebra, by
Joseph Mileti.
Group theory
-
Group (mathematics)
- Article from
Wikipedia.
See also
Group theory.
-
Open Problems in Combinatorial Group Theory
- Collected by G.Baumslag, A.Miasnikov and V.Shpilrain.
Ring theory and commutative algebra
-
Ring (mathematics)
- Article from
Wikipedia.
See also
Ring theory,
Commutative algebra.
Field theory
-
Field (mathematics)
- Article from
Wikipedia.
See also
Field theory,
Galois theory,
Finite field.
Linear algebra and matrix theory
-
Linear algebra
- Article from
Wikipedia.
See also
Matrix theory.
Algebra over a field,
Associative algebra
Category theory
-
Galaxy: Category Theory
- Categorized site directory. Entries usually include
descriptive annotations.
-
Category theory
- Article from
Wikipedia.
See also
Universal algebra,
Topos.
Miscellaneous algebra topics
-
Homological algebra
- Article from
Wikipedia.
-
K-theory
- Article from
Wikipedia.
- The Octonions
John C. Baez
Bulletin of the AMS, April 2002, pp. 145-205
- There are only four normed divisions algebras: the real numbers,
the complex numbers, the quaternions, and the octonions. The latter
bridge many areas of mathematics, such as Clifford algebras and
spinors, Bott periodicity, projective and Lorentzian geometry,
Jordan algebras, and exceptional Lie groups. The also appear in
theoretical physics in connectin with quantum logic, special
relativity, and supersymmetry.
[Abstract, references, downloadable text]
- Recent Developments in the Cohomology of Finite Groups
Alejandro Adem
Notices of the AMS, August 1997, pp. 806-812
- Cohomology of finite groups can be described completely
algebraically, but it can also be described in topological
terms. It forms an important bridge between algebra and topology
and touches a number of areas of mathematics. There are now a
number of ways to compute group cohomology.
[Article in PDF format]
- An Introduction to Computational Group Theory
Ákos Seress
Notices of the AMS, June/July 1997, pp. 671-679
- Computational group theory is one of the oldest and most
developed branches of computational algebra. Different techniques
and problems are associated with specific types, of groups,
such as finitely presented groups, polycyclic groups, permutation
groups, and matrix groups.
[Article in PDF format]
- On Finite Simple Groups and Their Classification
Ron Solomon
Notices of the AMS, February 1995, pp. 231-239
- Although the classification theorem for finite simple groups
was felt to be complete in 1983, and in spite of about 15,000
pages devoted to the proof, not all details had been
published, and loose ends remained. Since then, efforts have
continued to clean up the classification and address new problems
that it suggested. Interesting questions remain, especially
with respect to the sporadic simple groups, and the "Monster"
in particular.
[Article in PDF format]
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