Some properties of prime near-rings with -derivation.
An associated ring R with identity is said to be a left FTF ring when the class of the submodules of flat left R-modules is closed under injective hulls and direct products. We prove (Theorem 3.5) that a strongly graded ring R by a locally finite group G is FTF if and only if Re is left FTF, where e is a neutral element of G. This provides new examples of left FTF rings. Some consequences of this Theorem are given.
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.