The nil radical of an Archimedean partially ordered ring with positive squares
Lavrič, Boris
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 231-238 / Harvested from Czech Digital Mathematics Library
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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 $a_1a_2=a_2a_1=0$.

Publié le : 1994-01-01
Classification:  06F25,  16N40,  16W80 
@article{118661,
     author = {Boris Lavri\v c},
     title = {The nil radical of an Archimedean partially ordered ring with positive squares},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {231-238},
     zbl = {0805.06017},
     mrnumber = {1286569},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118661}
}

Lavrič, Boris. The nil radical of an Archimedean partially ordered ring with positive squares. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 231-238. http://gdmltest.u-ga.fr/item/118661/

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