Geodesic
The nil radical of an Archimedean partially ordered ring with positive squares
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 231-238 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $R$ be an Archimedean partially ordered ring in which the square of every element is positive, and $N(R)$ the set of all nilpotent elements of $R$. It is shown that $N(R)$ is the unique nil radical of $R$, and that $N(R)$ is locally nilpotent and even nilpotent with exponent at most $3$ when $R$ is 2-torsion-free. $R$ is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element $a$ is expressed as $a=a_1-a_2$ with positive $a_1$, $a_2$ satisfying $a_1a_2=a_2a_1=0$.
Let $R$ be an Archimedean partially ordered ring in which the square of every element is positive, and $N(R)$ the set of all nilpotent elements of $R$. It is shown that $N(R)$ is the unique nil radical of $R$, and that $N(R)$ is locally nilpotent and even nilpotent with exponent at most $3$ when $R$ is 2-torsion-free. $R$ is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element $a$ is expressed as $a=a_1-a_2$ with positive $a_1$, $a_2$ satisfying $a_1a_2=a_2a_1=0$.
Classification : 06F25, 16N40, 16W80
Keywords: partially ordered ring; Archimedean; nil radical; nilpotent 
@article{CMUC_1994_35_2_a2,
     author = {Lavri\v{c}, Boris},
     title = {The nil radical of an {Archimedean} partially ordered ring with positive squares},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {231--238},
     year = {1994},
     volume = {35},
     number = {2},
     mrnumber = {1286569},
     zbl = {0805.06017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1994_35_2_a2/}
}
TY  - JOUR
AU  - Lavrič, Boris
TI  - The nil radical of an Archimedean partially ordered ring with positive squares
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1994
SP  - 231
EP  - 238
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1994_35_2_a2/
LA  - en
ID  - CMUC_1994_35_2_a2
ER  - 
%0 Journal Article
%A Lavrič, Boris
%T The nil radical of an Archimedean partially ordered ring with positive squares
%J Commentationes Mathematicae Universitatis Carolinae
%D 1994
%P 231-238
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1994_35_2_a2/
%G en
%F CMUC_1994_35_2_a2
Lavrič, Boris. The nil radical of an Archimedean partially ordered ring with positive squares. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 231-238. http://geodesic.mathdoc.fr/item/CMUC_1994_35_2_a2/