# Embedding sums of cancellative modes into semimodules

Anna B. Romanowska; Anna Zamojska-Dzienio

Czechoslovak Mathematical Journal (2005)

- Volume: 55, Issue: 4, page 975-991
- ISSN: 0011-4642

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topRomanowska, Anna B., and Zamojska-Dzienio, Anna. "Embedding sums of cancellative modes into semimodules." Czechoslovak Mathematical Journal 55.4 (2005): 975-991. <http://eudml.org/doc/31004>.

@article{Romanowska2005,

abstract = {A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.},

author = {Romanowska, Anna B., Zamojska-Dzienio, Anna},

journal = {Czechoslovak Mathematical Journal},

keywords = {modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules},

language = {eng},

number = {4},

pages = {975-991},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Embedding sums of cancellative modes into semimodules},

url = {http://eudml.org/doc/31004},

volume = {55},

year = {2005},

}

TY - JOUR

AU - Romanowska, Anna B.

AU - Zamojska-Dzienio, Anna

TI - Embedding sums of cancellative modes into semimodules

JO - Czechoslovak Mathematical Journal

PY - 2005

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 55

IS - 4

SP - 975

EP - 991

AB - A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.

LA - eng

KW - modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules; modes (idempotent and entropic algebras); cancellative modes; sums of algebras; embeddings; semimodules over semirings; idempotent subreducts of semimodules

UR - http://eudml.org/doc/31004

ER -

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