The algebra of mode homomorphisms

Kira V. Adaricheva, Anna B. Romanowska, Jonathan D H Smith

    Research output: Contribution to journal › Article

    Abstract

    Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.

    Original languageEnglish
    Pages (from-to)1265-1277
    Number of pages13
    JournalCentral European Journal of Mathematics
    Volume12
    Issue number8
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Homomorphisms
    Algebra
    Idempotent
    Homomorphism

    Keywords

    • Affine space
    • Convex set
    • Mode
    • Płonka sum
    • Semilattice
    • Variety regularization

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Adaricheva, K. V., Romanowska, A. B., & Smith, J. D. H. (2014). The algebra of mode homomorphisms. Central European Journal of Mathematics, 12(8), 1265-1277. https://doi.org/10.2478/s11533-014-0405-2

    The algebra of mode homomorphisms. / Adaricheva, Kira V.; Romanowska, Anna B.; Smith, Jonathan D H.

    In: Central European Journal of Mathematics, Vol. 12, No. 8, 2014, p. 1265-1277.

    Research output: Contribution to journal › Article

    Adaricheva, KV, Romanowska, AB & Smith, JDH 2014, 'The algebra of mode homomorphisms', Central European Journal of Mathematics, vol. 12, no. 8, pp. 1265-1277. https://doi.org/10.2478/s11533-014-0405-2
    Adaricheva KV, Romanowska AB, Smith JDH. The algebra of mode homomorphisms. Central European Journal of Mathematics. 2014;12(8):1265-1277. https://doi.org/10.2478/s11533-014-0405-2
    Adaricheva, Kira V. ; Romanowska, Anna B. ; Smith, Jonathan D H. / The algebra of mode homomorphisms. In: Central European Journal of Mathematics. 2014 ; Vol. 12, No. 8. pp. 1265-1277.
    @article{3982090019db4824a59a001128eb14f7,
    title = "The algebra of mode homomorphisms",
    abstract = "Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.",
    keywords = "Affine space, Convex set, Mode, Płonka sum, Semilattice, Variety regularization",
    author = "Adaricheva, {Kira V.} and Romanowska, {Anna B.} and Smith, {Jonathan D H}",
    year = "2014",
    doi = "10.2478/s11533-014-0405-2",
    language = "English",
    volume = "12",
    pages = "1265--1277",
    journal = "Open Mathematics",
    issn = "1895-1074",
    publisher = "Walter de Gruyter GmbH & Co. KG",
    number = "8",

    }

    TY - JOUR

    T1 - The algebra of mode homomorphisms

    AU - Adaricheva, Kira V.

    AU - Romanowska, Anna B.

    AU - Smith, Jonathan D H

    PY - 2014

    Y1 - 2014

    N2 - Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.

    AB - Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism algebras. Some critical examples are examined.

    KW - Affine space

    KW - Convex set

    KW - Mode

    KW - Płonka sum

    KW - Semilattice

    KW - Variety regularization

    UR - http://www.scopus.com/inward/record.url?scp=84899950051&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84899950051&partnerID=8YFLogxK

    U2 - 10.2478/s11533-014-0405-2

    DO - 10.2478/s11533-014-0405-2

    M3 - Article

    AN - SCOPUS:84899950051

    VL - 12

    SP - 1265

    EP - 1277

    JO - Open Mathematics

    JF - Open Mathematics

    SN - 1895-1074

    IS - 8

    ER -

    Access to Document