The algebra of mode homomorphisms

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

Research output: Contribution to journalArticle

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 - Aug 2014

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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