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Results tagged with ra.rings-and-algebras
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user 28104
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
6
votes
Accepted
Can a block matrix with at least 3 zero blocks of different size on the diagonal and 1's eve...
There are some quantifiers unclear in your question, but regardless of how
to read it, your assertion is false. -- The smallest counterexample with
blocks of pairwise distinct size all of whose eigen …
- 19.6k
3
votes
Units in a group algebra
Even if $k = \mathbb{F}_p$ for some prime $p$ and $G$ is a $p$-group, it is certainly not easy to describe the group of units of the modular group algebra $kG$. -- For example the Modular Isomorphism …
- 19.6k
16
votes
0
answers
779
views
How to explain the picturesque patterns in François Brunault's matrix?
How to explain the patterns in the matrix defined in François Brunault's
answer to the question Freeness of a Z[x] module depicted below? --
Choosing colors according to the highest power of 2 which …
- 19.6k
22
votes
4
answers
2k
views
Freeness of a Z[x]-module
Definition: Call a mapping $f: \mathbb{Z} \rightarrow \mathbb{Z}$
a generalized polynomial if for any distinct integers $m$ and $n$
we have $(m - n)|(f(m)-f(n))$.
It is easy to check that polynomial …
- 19.6k
13
votes
Accepted
The set of orders of elements in a group
Obviously not for every set $A \subset \mathbb{N}$ there is a group $G$ with $A$ as
set of orders of its elements (usually called 'spectrum') -- for example if $G$ has an element of order $n$, then $G …
- 19.6k