Rings of maps: sequential convergence and completion

Roman Frič

Displaying similar documents to “Rings of maps: sequential convergence and completion”

Pointwise convergence fails to be strict

Ján Borsík, Roman Frič (1998)

Czechoslovak Mathematical Journal

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It is known that the ring $B (ℝ)$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $C (ℝ)$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $C (ℝ)$ . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $C (ℝ)$ which differs from $B (ℝ)$ .

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring $(HR, ω)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring $R$ satisfies McCoy’s theorem of skew Hurwitz series.

A completion of $ℤ$ is a field

José E. Marcos (2003)

Czechoslovak Mathematical Journal

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We define various ring sequential convergences on $ℤ$ and $ℚ$ . We describe their properties and properties of their convergence completions. In particular, we define a convergence $𝕃_{1}$ on $ℤ$ by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields $ℤ / (p)$ . Further, we show that $(ℤ, 𝕃_{1}^{*})$ is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan. ...

Displaying similar documents to “Rings of maps: sequential convergence and completion”

Pointwise convergence fails to be strict

On a theorem of McCoy

A completion of ℤ is a field

A completion of $ℤ$ is a field