# The algebra of mode homomorphisms

Kira Adaricheva; Anna Romanowska; Jonathan Smith

Open Mathematics (2014)

- Volume: 12, Issue: 8, page 1265-1277
- ISSN: 2391-5455

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topKira Adaricheva, Anna Romanowska, and Jonathan Smith. "The algebra of mode homomorphisms." Open Mathematics 12.8 (2014): 1265-1277. <http://eudml.org/doc/269651>.

@article{KiraAdaricheva2014,

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.},

author = {Kira Adaricheva, Anna Romanowska, Jonathan Smith},

journal = {Open Mathematics},

keywords = {Mode; Convex set; Affine space; Semilattice; Variety regularization; Płonka sum; modes; semilattices; variety regularizations; Płonka sums},

language = {eng},

number = {8},

pages = {1265-1277},

title = {The algebra of mode homomorphisms},

url = {http://eudml.org/doc/269651},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Kira Adaricheva

AU - Anna Romanowska

AU - Jonathan Smith

TI - The algebra of mode homomorphisms

JO - Open Mathematics

PY - 2014

VL - 12

IS - 8

SP - 1265

EP - 1277

AB - 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.

LA - eng

KW - Mode; Convex set; Affine space; Semilattice; Variety regularization; Płonka sum; modes; semilattices; variety regularizations; Płonka sums

UR - http://eudml.org/doc/269651

ER -

## References

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- [8] Romanowska A.B., Smith J.D.H., Modal Theory, Res. Exp. Math., 9, Heldermann, Berlin, 1985
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