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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.

Image d'un homomorphisme et flot des poids d'une relation d'Équivalence mesurée.

Jean-Luc Sauvageot (1978)

Mathematica Scandinavica

Implementation canonique pour les co-actions d'un groupe localement compact et les systèmes dynamiques generalises.

Jean-Luc Sauvageot (1985)

Mathematische Annalen

Induced and amenable ergodic actions of Lie groups

Robert J. Zimmer (1978)

Annales scientifiques de l'École Normale Supérieure

Induced C*-Algebras and a Symmetric Imprimitivity Theorem.

Iain Raeburn (1988)

Mathematische Annalen

Induced representations and classification for $G S p (2, F)$ and $S p (2, F)$

Paul J.jun. Sally, Marko Tadic (1993)

Mémoires de la Société Mathématique de France

Induced representations and duality results for commutative hypergroups.

Michael Voit, Peter Hermann (1995)

Forum mathematicum

Induced Representations and Hypergroup Homomorphisms.

Peter Hermann (1993)

Monatshefte für Mathematik

Induced representations of completely solvable Lie groups

Ronald L. Lipsman (1990)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Induced representations of groupoid crossed products.

Amini, Massoud (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Induced representations of hypergroups.

Peter Hermann (1992)

Mathematische Zeitschrift

Induction and restriction as adjoint functors on representations of locally compact groups.

Bekes, Robert A., Hilton, Peter J. (1993)

International Journal of Mathematics and Mathematical Sciences

Induction from a normal nilpotent subgroup

N. Giovannini (1977)

Annales de l'I.H.P. Physique théorique

Inductive extreme non-Arens regularity of the Fourier algebra A(G)

Zhiguo Hu (2002)

Studia Mathematica

Let G be a non-discrete locally compact group, A(G) the Fourier algebra of G, VN(G) the von Neumann algebra generated by the left regular representation of G which is identified with A(G)*, and WAP(Ĝ) the space of all weakly almost periodic functionals on A(G). We show that there exists a directed family ℋ of open subgroups of G such that: (1) for each H ∈ ℋ, A(H) is extremely non-Arens regular; (2) $V N (G) = ⋃_{H \in ℋ} V N (H)$ and $V N (G) / W A P (G ̂) = ⋃_{H \in ℋ} [V N (H) / W A P (H ̂)]$ ; (3) $A (G) = ⋃_{H \in ℋ} A (H)$ and it is a WAP-strong inductive union in the sense that the unions in (2) are strongly...

Infinite ergodic index $ℤ^{d}$ -actions in infinite measure

E. Muehlegger, A. Raich, C. Silva, M. Touloumtzis, B. Narasimhan, W. Zhao (1999)

Colloquium Mathematicae

We construct infinite measure preserving and nonsingular rank one $ℤ^{d}$ -actions. The first example is ergodic infinite measure preserving but with nonergodic, infinite conservative index, basis transformations; in this case we exhibit sets of increasing finite and infinite measure which are properly exhaustive and weakly wandering. The next examples are staircase rank one infinite measure preserving $ℤ^{d}$ -actions; for these we show that the individual basis transformations have conservative ergodic Cartesian...

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