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Results tagged with ra.rings-and-algebras
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user 17263
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.
2
votes
Is there a name for this map induced by bilinear forms?
A bilinear form on $V$ (if non-degenerate) lets you identify $V$ with $V^\star$:
$v \mapsto \langle v, \cdot \rangle$
In this case, your map is just a contraction of the identity map on $V^\star \oti …
- 1,197
14
votes
1
answer
4k
views
Do these matrix rings have non-zero elements that are neither units nor zero divisors?
First, a disclaimer: This is a repost of a question I asked on stackexchange (no answer there).
Let $R$ be a commutative ring (with $1$) and $R^{n \times n}$ be the ring of $n \times n$ matrices with …
- 1,197
5
votes
2
answers
781
views
When does End(M) consist entirely of zero, zero divisors, and units?
Let $R$ be a commutative ring (with $1$) such that every non-zero divisor in $R$ is a unit (see Rings in which every non-unit is a zero divisor for various stabs at what these are called). Let $M$ be …
- 1,197
6
votes
2
answers
557
views
Given 2 towers of fields, when are these fields isomorphic?
Let $F_0 \subset F_1 \subset F_2 \subset \cdots$ and $K_0 \subset K_1 \subset K_2 \subset \cdots$ be two towers of fields. Also, let $F = \cup_{i=0}^\infty F_i$ and $K = \cup_{i=0}^\infty K_i$.
Now s …
- 1,197