• Title, Summary, Keyword: countable ring

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Simple Presentness in Modular Group Algebras over Highly-generated Rings

  • Danchev, Peter V.
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.57-64
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    • 2006
  • It is proved that if G is a direct sum of countable abelian $p$-groups and R is a special selected commutative unitary highly-generated ring of prime characteristic $p$, which ring is more general than the weakly perfect one, then the group of all normed units V (RG) modulo G, that is V (RG)=G, is a direct sum of countable groups as well. This strengthens a result due to W. May, published in (Proc. Amer. Math. Soc., 1979), that treats the same question but over a perfect ring.

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INTEGRAL OPERATORS FOR OPERATOR VALUED MEASURES

  • Park, Jae-Myung
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.331-336
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    • 1994
  • Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

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SKEW POWER SERIES EXTENSIONS OF α-RIGID P.P.-RINGS

  • Hashemi, Ebrahim;Moussavi, Ahmad
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.657-664
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    • 2004
  • We investigate skew power series of $\alpha$-rigid p.p.-rings, where $\alpha$ is an endomorphism of a ring R which is not assumed to be surjective. For an $\alpha$-rigid ring R, R[[${\chi};{\alpha}$]] is right p.p., if and only if R[[${\chi},{\chi}^{-1};{\alpha}$]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).