Affine regular decagons in GS-quasigroup

Vladimír Volenec; Zdenka Kolar-Begović

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 3, page 383-395
  • ISSN: 0010-2628

Abstract

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In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup ℂ ( 1 2 ( 1 + 5 ) ) .

How to cite

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Volenec, Vladimír, and Kolar-Begović, Zdenka. "Affine regular decagons in GS-quasigroup." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 383-395. <http://eudml.org/doc/23010>.

@article{Volenec2008,
abstract = {In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup $\mathbb \{C\}(\frac\{1\}\{2\}(1+\sqrt\{5\}))$.},
author = {Volenec, Vladimír, Kolar-Begović, Zdenka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {GS-quasigroup; affine regular decagon; affine regular pentagon; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties},
language = {eng},
number = {3},
pages = {383-395},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Affine regular decagons in GS-quasigroup},
url = {http://eudml.org/doc/23010},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Volenec, Vladimír
AU - Kolar-Begović, Zdenka
TI - Affine regular decagons in GS-quasigroup
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 3
SP - 383
EP - 395
AB - In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup $\mathbb {C}(\frac{1}{2}(1+\sqrt{5}))$.
LA - eng
KW - GS-quasigroup; affine regular decagon; affine regular pentagon; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties
UR - http://eudml.org/doc/23010
ER -

References

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  1. Volenec V., GS-quasigroups, Časopis Pěst. Mat. 115 (1990), 307-318. (1990) Zbl0715.20044MR1071063
  2. Kolar Z., Volenec V., GS-trapezoids in GS-quasigroups, Math. Commun. 7 (2002), 143-158. (2002) Zbl1016.20052MR1952756
  3. Kolar-Begović Z., Volenec V., DGS-trapezoids in GS-quasigroups, Math. Commun. 8 (2003), 215-218. (2003) Zbl1061.20062MR2026399
  4. Kolar-Begović Z., Volenec V., Affine regular pentagons in GS-quasigroups, Quasigroups Related Systems 12 (2004), 103-112. (2004) Zbl1073.20062MR2130583
  5. Kolar-Begović Z., Volenec V., GS-deltoids in GS-quasigroups, Math. Commun. 10 (2005), 117-122. (2005) Zbl1089.20039MR2199101

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