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Some Algebraic Aspects of Boolean Valued Analysis

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Operator Theory and Harmonic Analysis (OTHA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 357))

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Abstract

The article deals with a Boolean valued approach to some algebraic problems arising from functional analysis. The main results are as follows. (1) A universally complete vector lattice without locally one-dimensional bands contains an infinite direct sum of order dense sublattices each of which is a band preserving linear isomorphic (but not lattice isomorphic) copy of the whole lattice. (2) Every separated injective module over a semiprime rationally complete commutative ring admits a direct sum decomposition with homogeneous summands. (3) A semiprime rationally complete commutative ring properly embedded in a ring with projections K is a homogeneity ring of an additive mapping between appropriate K-modules.

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Author information

Authors and Affiliations

  1. Southern Mathematical Institute of the Vladikavkaz Scientific Center of the RAS, Vladikavkaz, Russia

    Anatoly G. Kusraev

  2. K. L. Khetagurov North-Ossetian State University, Vladikavkaz, Russia

    Anatoly G. Kusraev

Authors
  1. Anatoly G. Kusraev
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Correspondence to Anatoly G. Kusraev .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Mechanic and Computer Sciences and Regional Mathematical Center, Southern Federal University, Rostov-on-Don, Russia

    Alexey N. Karapetyants

  2. Department of Mathematics, Cinvestav, Santiago de Queretaro, Querétaro, Mexico

    Vladislav V. Kravchenko

  3. Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Elijah Liflyand

  4. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Helmuth R. Malonek

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Kusraev, A.G. (2021). Some Algebraic Aspects of Boolean Valued Analysis. In: Karapetyants, A.N., Kravchenko, V.V., Liflyand, E., Malonek, H.R. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-030-77493-6_19

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