A characterization of finite Stone pseudocomplemented ordered sets
Mathematica Bohemica (1996)
- Volume: 121, Issue: 2, page 117-120
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topHalaš, Radomír. "A characterization of finite Stone pseudocomplemented ordered sets." Mathematica Bohemica 121.2 (1996): 117-120. <http://eudml.org/doc/247985>.
@article{Halaš1996,
abstract = {A distributive pseudocomplemented set $S$ [2] is called Stone if for all $a\in S$ the condition $LU(a^*,a^\{**\})=S$ holds. It is shown that in a finite case $S$ is Stone iff the join of all distinct minimal prime ideals of $S$ is equal to $S$.},
author = {Halaš, Radomír},
journal = {Mathematica Bohemica},
keywords = {Stone ordered set; prime ideal; distributive pseudocomplemented ordered set; $l$-ideal; Stone ordered set; prime ideal; distributive pseudocomplemented ordered set},
language = {eng},
number = {2},
pages = {117-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A characterization of finite Stone pseudocomplemented ordered sets},
url = {http://eudml.org/doc/247985},
volume = {121},
year = {1996},
}
TY - JOUR
AU - Halaš, Radomír
TI - A characterization of finite Stone pseudocomplemented ordered sets
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 2
SP - 117
EP - 120
AB - A distributive pseudocomplemented set $S$ [2] is called Stone if for all $a\in S$ the condition $LU(a^*,a^{**})=S$ holds. It is shown that in a finite case $S$ is Stone iff the join of all distinct minimal prime ideals of $S$ is equal to $S$.
LA - eng
KW - Stone ordered set; prime ideal; distributive pseudocomplemented ordered set; $l$-ideal; Stone ordered set; prime ideal; distributive pseudocomplemented ordered set
UR - http://eudml.org/doc/247985
ER -
References
top- Grätzer G., Schmidt E. T., 10.1007/BF02020328, Acta Math. Sci. Hungarica 8 (1957), 455-460. (1957) MR0092763DOI10.1007/BF02020328
- Halaš R., Pseudocomplemented ordered sets, Arch. Math. (Brno) 29 (1993), no. 3-4, 153-160. (1993) MR1263116
- Halaš R., Ideals, polars and annihilators in ordered sets, PҺD thesis, Olomouc, 1994. (1994)
- Chajda I., Complemented ordered sets, Aгch. Math. (Brno) 28 (1992), 25-34. (1992) Zbl0785.06002MR1201863
- Chajda I., Rachůnek J., 10.1007/BF00353659, Order 5 (1989), 407-423. (1989) MR1010389DOI10.1007/BF00353659
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.