# Category:Rings of Sequences

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This category contains results about Rings of Sequences.

Definitions specific to this category can be found in Definitions/Rings of Sequences.

Let $\struct {R, +, \circ}$ be a ring.

Given the natural numbers $\N$, the **ring of sequences over $R$** is the ring of mappings $\struct {R^\N, +', \circ'}$ where:

- $(1): \quad R^\N$ is the set of sequences in $R$
- $(2): \quad +'$ and $\circ'$ are the (pointwise) operations induced by $+$ and $\circ$.

## Pages in category "Rings of Sequences"

The following 12 pages are in this category, out of 12 total.

### L

- Leigh.Samphier/Sandbox/Addition of Quotient Ring of Cauchy Sequences
- Leigh.Samphier/Sandbox/Definition:Induced Norm on Quotient of Cauchy Sequences
- Leigh.Samphier/Sandbox/Definition:Normed Quotient of Cauchy Sequences
- Leigh.Samphier/Sandbox/Embedding Division Ring into Quotient Ring of Cauchy Sequences
- Leigh.Samphier/Sandbox/Product of Quotient Ring of Cauchy Sequences
- Leigh.Samphier/Sandbox/Quotient Ring of Cauchy Sequences is Division Ring
- Leigh.Samphier/Sandbox/Quotient Ring of Cauchy Sequences is Division Ring/Corollary 1
- Leigh.Samphier/Sandbox/Quotient Ring of Cauchy Sequences is Normed Division Ring
- Leigh.Samphier/Sandbox/Unity of Quotient Ring of Cauchy Sequences
- Leigh.Samphier/Sandbox/Zero of Quotient Ring of Cauchy Sequences