Symbols:A/Ann
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Annihilator of Ring
- $\operatorname {Ann}$
Let $B: R \times \Z$ be a bilinear mapping defined as:
- $B: R \times \Z: \tuple {r, n} \mapsto n \cdot r$
where $n \cdot r$ defined as an integral multiple of $r$:
- $n \cdot r = r + r + \cdots \paren n \cdots r$
Note the change of order of $r$ and $n$:
- $\map B {r, n} = n \cdot r$
Let $D \subseteq R$ be a subring of $R$.
Then the annihilator of $D$ is defined as:
- $\map {\mathrm {Ann} } D = \set {n \in \Z: \forall d \in D: n \cdot d = 0_R}$
or, when $D = R$:
- $\map {\mathrm {Ann} } R = \set {n \in \Z: \forall r \in R: n \cdot r = 0_R}$
Its $\LaTeX$ code is \operatorname {Ann}
.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Ann