Displaying 341 – 360 of 510

Showing per page

The nil radical of an Archimedean partially ordered ring with positive squares

Boris Lavrič (1994)

Commentationes Mathematicae Universitatis Carolinae

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 ,...

Currently displaying 341 – 360 of 510