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Let and be two ring homomorphisms and let and be two ideals of and , respectively, such that . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring of with along with respect to .
The aim of this work is to describe the irreducible components of the nilpotent complex associative algebras varieties of dimension 2 to 5 and to give a lower bound of the number of these components in any dimension.
Let be an Archimedean partially ordered ring in which the square of every element is positive, and the set of all nilpotent elements of . It is shown that is the unique nil radical of , and that is locally nilpotent and even nilpotent with exponent at most when is 2-torsion-free. 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 is expressed as with positive ,...
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