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A completion of ℤ is a field

José E. Marcos (2003)

Czechoslovak Mathematical Journal

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.

Idempotents and the multiplicative group of some totally bounded rings

Mohamed A. Salim, Adela Tripe (2011)

Czechoslovak Mathematical Journal

In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2 ℵ 0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

Locally compact modules over compact rings

Nicola Rodinò (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Sia A un anello compatto e sia M un A -modulo localmente compatto. Le dimostrazioni note che M è linearmente topologizzato sembrano alquanto involute ed usano risultati profondi della teoria dei gruppi Abeliani localmente compatti nonché il Teorema di Kaplansky che asserisce che A è linearmente topologizzato. In questa Nota, poggiando sul Teorema di Peter-Weyl, viene esposta una dimostrazione semplice e diretta, della quale il Teorema di Kaplansky è corollario.

On the rings of formal solutions of polynomial differential equations

Maria-Angeles Zurro (1998)

Banach Center Publications

The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.

On the Weierstrass division.

Łojasiewicz, Stanisław, Maszczyk, Tomasz, Rusek, Kamil (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi (2003)

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of quasi-homeomorphisms, the Goldman prime spectrum and the Jacobson prime spectrum of a commutative ring. We prove that, if g : Y → X is a quasi-homeomorphism, Z a sober space and f : Y → Z a continuous map, then there exists a unique continuous map F : X → Z such that F ∘ g = f . Let X be a T 0 -space, q : X → s X the injection of X onto its sobrification X s . It is shown, here, that q ⁢ Gold ⁢ X = Gold ⁢ X s , where Gold ⁢ X is the set of all locally closed points of X . Some applications are also indicated. The Jacobson prime spectrum...

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