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 $\circ$.