• DocumentCode
    3022655
  • Title

    Multiplicative band semirings and distributive lattices

  • Author

    Zhu, Tianmin ; Yu, Baomin

  • Author_Institution
    Inst. of Math. & Appl. Math., Weinan Teachers Univ., Weinan, China
  • fYear
    2011
  • fDate
    26-28 July 2011
  • Firstpage
    2206
  • Lastpage
    2208
  • Abstract
    In this paper, we investigate multiplicative semirings with identity element. From the algebraic properties of lattices and distributive lattices, we study some properties of multiplicatice semirngs with identity. We show that if S, which is a semirings with identity, is a multiplicative band semiring if and only if S is a distributive lattice. Finally, we obtain a representation theorem for distributive lattices.
  • Keywords
    lattice theory; set theory; algebraic properties; distributive lattices; multiplicative band semirings; representation theorem; Absorption; Abstract algebra; Additives; Lattices; Presses; Upper bound; distributive lattice; identity element; multiplicative band semiring;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Multimedia Technology (ICMT), 2011 International Conference on
  • Conference_Location
    Hangzhou
  • Print_ISBN
    978-1-61284-771-9
  • Type

    conf

  • DOI
    10.1109/ICMT.2011.6001714
  • Filename
    6001714
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3022655