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 › peer-review

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

Keywords

Affine space
Convex set
Mode
Płonka sum
Semilattice
Variety regularization

ASJC Scopus subject areas

Mathematics(all)

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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 P{\l}onka sums of more elementary homomorphism algebras. Some critical examples are examined.",

keywords = "Affine space, Convex set, Mode, P{\l}onka sum, Semilattice, Variety regularization",

author = "Adaricheva, {Kira V.} and Romanowska, {Anna B.} and Smith, {Jonathan D.H.}",

note = "Funding Information: This research was supported by the Warsaw University of Technology under grant number 504G/1120/0054/000. Work on this paper was conducted during visits of the first author to Iowa State University in 2007, the second author to Iowa State University in 2010–12, and the third author to the Warsaw University of Technology in 2012–13.",

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AU - Adaricheva, Kira V.

AU - Romanowska, Anna B.

AU - Smith, Jonathan D.H.

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KW - Affine space

KW - Convex set

KW - Mode

KW - Płonka sum

KW - Semilattice

KW - Variety regularization

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