Sturdy frames of type $(2,2)$ algebras and their applications to semirings

Volume 179 / 2003

X. Z. Zhao, Y. Q. Guo, K. P. Shum Fundamenta Mathematicae 179 (2003), 69-81 MSC: 16Y60, 08B25, 20M07. DOI: 10.4064/fm179-1-6

Abstract

We introduce sturdy frames of type $(2,2)$ algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.

Authors

  • X. Z. ZhaoDepartment of Mathematics
    Northwest University
    Xi'an, Shanxi, 710069, P.R. China
    e-mail
  • Y. Q. GuoInstitute of Mathematics
    Southwest China Normal University
    Beibei, Chongqing 400715, P.R. China
    e-mail
  • K. P. ShumScience Faculty
    The Chinese University of Hong Kong
    Shatin, Hong Kong
    e-mail

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