# Category:Definitions/Rings of Sequences

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This category contains definitions related to Rings of Sequences.

Related results can be found in Category: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 "Definitions/Rings of Sequences"

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

### P

### R

- Definition:Ring of Cauchy Sequences
- Definition:Ring of Sequences
- Definition:Ring of Sequences of Finite Support
- Definition:Ring of Sequences/Additive Inverse
- Definition:Ring of Sequences/Commutativity
- Definition:Ring of Sequences/Pointwise Addition
- Definition:Ring of Sequences/Pointwise Multiplication
- Definition:Ring of Sequences/Units
- Definition:Ring of Sequences/Unity
- Definition:Ring of Sequences/Zero