The algebra of mode homomorphisms

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

doi:10.2478/s11533-014-0405-2

The algebra of mode homomorphisms

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

Department of Mathematics

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 language	English
Pages (from-to)	1265-1277
Number of pages	13
Journal	Central European Journal of Mathematics
Volume	12
Issue number	8
DOIs	https://doi.org/10.2478/s11533-014-0405-2
Publication status	Published - 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

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Access to Document

10.2478/s11533-014-0405-2