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Results tagged with ra.rings-and-algebras
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user 5963
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.
11
votes
Accepted
Are the banded versions of a positive definite matrix positive definite?
No. The matrix
$M = \begin{bmatrix}5 & 4 & 4 \\\\ 4 & 5 & 4 \\\\ 4 & 4 & 5\end{bmatrix} = \begin{bmatrix}2 & 2 & 2\end{bmatrix}\begin{bmatrix}2 \\\\ 2 \\\\ 2\end{bmatrix} + I$
is positive definite, …
- 8,501
10
votes
4
answers
1k
views
Groups and rings which are not sets
An algebraic structure such as a group, ring, field, etc. is usually defined to be a set with some operations satisfying certain properties. I am curious what, if anything, goes wrong when the underl …
- 8,501
9
votes
Accepted
Semiring naturally associated to any monoid?
It is at least sometimes called a "monoid semiring" by analogy with "group ring". As such it would be notated $S = \mathbb{N_0}[M]$ (or $\mathbb{N}[M]$ depending how you define things).
By the way, …
- 8,501
7
votes
Computer algebra systems that can handle real-closed fields?
Not really useful enough for an answer, but a little long to be a comment:
While it is true that you can introduce extra variables and constrain their squares to be the quantities which you wish to b …
- 8,501
2
votes
Other Ring Structures on $\mathbb{Q}$
Since the question is somewhat fuzzy, I am not 100% sure what would satisfy you as an answer. Based on nothing, I am guessing you want something a little stranger than the examples Neil and Pace have …
- 8,501