Radical decompositions of semiheaps

Ian Hawthorn; Tim Stokes

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 2, page 191-208
  • ISSN: 0010-2628

Abstract

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Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading to a radical-theoretic interpretation of the largest idempotent-separating congruence.

How to cite

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Hawthorn, Ian, and Stokes, Tim. "Radical decompositions of semiheaps." Commentationes Mathematicae Universitatis Carolinae 50.2 (2009): 191-208. <http://eudml.org/doc/32493>.

@article{Hawthorn2009,
abstract = {Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading to a radical-theoretic interpretation of the largest idempotent-separating congruence.},
author = {Hawthorn, Ian, Stokes, Tim},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {radical theory of idempotent algebras; ternary operation; involuted semigroups; semiheaps; generalised heaps; heaps; semiheaps; generalized heaps; varieties of heaps; involuted semigroups; radicals; idempotent heaps; radical theory of idempotent algebras; ternary operations; radical classes; varieties of semigroups},
language = {eng},
number = {2},
pages = {191-208},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Radical decompositions of semiheaps},
url = {http://eudml.org/doc/32493},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Hawthorn, Ian
AU - Stokes, Tim
TI - Radical decompositions of semiheaps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 2
SP - 191
EP - 208
AB - Semiheaps are ternary generalisations of involuted semigroups. The first kind of semiheaps studied were heaps, which correspond closely to groups. We apply the radical theory of varieties of idempotent algebras to varieties of idempotent semiheaps. The class of heaps is shown to be a radical class, as are two larger classes having no involuted semigroup counterparts. Radical decompositions of various classes of idempotent semiheaps are given. The results are applied to involuted I-semigroups, leading to a radical-theoretic interpretation of the largest idempotent-separating congruence.
LA - eng
KW - radical theory of idempotent algebras; ternary operation; involuted semigroups; semiheaps; generalised heaps; heaps; semiheaps; generalized heaps; varieties of heaps; involuted semigroups; radicals; idempotent heaps; radical theory of idempotent algebras; ternary operations; radical classes; varieties of semigroups
UR - http://eudml.org/doc/32493
ER -

References

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  11. Stokes T., 10.1007/s000120050082, Algebra Universalis 40 (1998), 73--85. Zbl0935.08004MR1643221DOI10.1007/s000120050082
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