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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 0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

Imposing psendocompact group topologies on Abeliau groups

W. Comfort, I. Remus (1993)

Fundamenta Mathematicae

The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m ( α ) 2 α . We show:    Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m ( α ) r 0 ( G ) γ 2 α , or α > ω and α ω r 0 ( G ) 2 α , then G admits a pseudocompact group topology of weight α.  Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies r 0 ( G ) m ( α ) .  Theorem 5.2(b). If G is divisible Abelian with 2 r 0 ( G ) γ , then G admits at most 2 γ -many...

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