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Lacunar ring topologies and maximum ring topologies with a prescribed convergent sequence

✍ Scribed by J.E. Marcos

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 255 KB
Volume: 162
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(00)00120-1

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✦ Synopsis

We show a ring topology on k[X ], which we call lacunar, whose completion is a subring of k[[X ]] consisting of some particular series with many zero coe cients. Zelenyuk, Protasov and Khromulyak have proven that each countable ring is complete with the ring topology which is maximum among those for which a certain T-sequence converges. We present some concrete examples of this situation on the rings k[X ], Z, k(X ) and Q.

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