Near heaps

Hawthorn, Ian, and Stokes, Tim. "Near heaps." Commentationes Mathematicae Universitatis Carolinae 52.2 (2011): 163-175. <http://eudml.org/doc/247208>.

@article{Hawthorn2011,
abstract = {On any involuted semigroup $(S,\cdot ,^\{\prime \})$, define the ternary operation $[abc]:=a\cdot b^\{\prime \}\cdot c$ for all $a,b,c\in S$. The resulting ternary algebra $(S,[ ])$ satisfies the para-associativity law $[[abc]de]= [a[dcb]e]= [ab[cde]]$, which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws $[aaa]= a$ and $[aab]= [baa]$. Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup operations are determined by the semiheap operation. We show that near heaps are exactly strong semilattices of heaps, parallelling a known result for Clifford semigroups. We characterise those near heaps which arise directly from Clifford semigroups, and show that all near heaps are embeddable in such examples, extending known results of this kind relating heaps to groups, generalised heaps to inverse semigroups, and general semiheaps to involuted semigroups.},
author = {Hawthorn, Ian, Stokes, Tim},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Clifford semigroups; semiheaps; generalised heaps; heaps; Clifford semigroups; variety of semiheaps; generalised heaps; variety of near heaps; involuted semigroups},
language = {eng},
number = {2},
pages = {163-175},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Near heaps},
url = {http://eudml.org/doc/247208},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Hawthorn, Ian
AU - Stokes, Tim
TI - Near heaps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 2
SP - 163
EP - 175
AB - On any involuted semigroup $(S,\cdot ,^{\prime })$, define the ternary operation $[abc]:=a\cdot b^{\prime }\cdot c$ for all $a,b,c\in S$. The resulting ternary algebra $(S,[ ])$ satisfies the para-associativity law $[[abc]de]= [a[dcb]e]= [ab[cde]]$, which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws $[aaa]= a$ and $[aab]= [baa]$. Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup operations are determined by the semiheap operation. We show that near heaps are exactly strong semilattices of heaps, parallelling a known result for Clifford semigroups. We characterise those near heaps which arise directly from Clifford semigroups, and show that all near heaps are embeddable in such examples, extending known results of this kind relating heaps to groups, generalised heaps to inverse semigroups, and general semiheaps to involuted semigroups.
LA - eng
KW - Clifford semigroups; semiheaps; generalised heaps; heaps; Clifford semigroups; variety of semiheaps; generalised heaps; variety of near heaps; involuted semigroups
UR - http://eudml.org/doc/247208
ER -