Flocks in universal and Boolean algebras

Gabriele Ricci

Discussiones Mathematicae - General Algebra and Applications (2010)

  • Volume: 30, Issue: 1, page 45-69
  • ISSN: 1509-9415

Abstract

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We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras, where flocks form "local" algebras with a sparseness similar to the one of vector spaces. We also outline the problem of generalizing the Segre transformations of based algebras, which used certain flocks, in order to approach a general transformation notion.

How to cite

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Gabriele Ricci. "Flocks in universal and Boolean algebras." Discussiones Mathematicae - General Algebra and Applications 30.1 (2010): 45-69. <http://eudml.org/doc/276552>.

@article{GabrieleRicci2010,
abstract = { We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras, where flocks form "local" algebras with a sparseness similar to the one of vector spaces. We also outline the problem of generalizing the Segre transformations of based algebras, which used certain flocks, in order to approach a general transformation notion. },
author = {Gabriele Ricci},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {combinators; elementary functions; closure system; interpolators; semi-affine lattice},
language = {eng},
number = {1},
pages = {45-69},
title = {Flocks in universal and Boolean algebras},
url = {http://eudml.org/doc/276552},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Gabriele Ricci
TI - Flocks in universal and Boolean algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 1
SP - 45
EP - 69
AB - We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras, where flocks form "local" algebras with a sparseness similar to the one of vector spaces. We also outline the problem of generalizing the Segre transformations of based algebras, which used certain flocks, in order to approach a general transformation notion.
LA - eng
KW - combinators; elementary functions; closure system; interpolators; semi-affine lattice
UR - http://eudml.org/doc/276552
ER -

References

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