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Symmetric and reversible properties of bi-amalgamated rings

Antonysamy Aruldoss, Chelliah Selvaraj (2024)

Czechoslovak Mathematical Journal

Let f : A → B and g : A → C be two ring homomorphisms and let K and K ' be two ideals of B and C , respectively, such that f - 1 ( K ) = g - 1 ( K ' ) . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring A ⋈ f , g ( K , K ' ) of A with ( B , C ) along ( K , K ' ) with respect to ( f , g ) .

The irreducible components of the nilpotent associative algebras.

Abdenacer Makhlouf (1993)

Revista Matemática de la Universidad Complutense de Madrid

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.

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 ,...

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