An element is known a strongly nil* clean if a=e1 - e1e2 + n , where e1,e2 are idempotents and nilpotent, that commute with one another. ideal I of ring R called each element. We investigate some its fundamental features, as well relationship to the nil ideal.

We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson radical of any locally finite profinite ring is nil of finite nilexponent. Our results apply to the context of small compact G-rings, where we also obtain a...

We construct a nil ring R which has bounded index of nilpotence 2, is Wedderburn radical, and is commutative, and which also has a derivation δ for which the differential polynomial ring R[x; δ] is not even prime radical. This example gives a strong barrier to lifting certain radical properties from rings to differential polynomial rings. It also demarcates the strength of recent results about ...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

The following theorem is proved: Let R be an algebra with involution over an uncountable field F. Then if the symmetric elements of R are algebraic, R is algebraic. In this paper we consider the following question: "Let R be an algebra with involution over a field F, and assume that the symmetric elements S of R are algebraic over F. Is R algebraic over FT* Previous results related to this ques...

A new class of rings, the class of weakly left localizable rings, is introduced. A ring R is called weakly left localizable if each non-nilpotent element of R is invertible in some left localization SR of the ring R. Explicit criteria are given for a ring to be a weakly left localizable ring provided the ring has only finitely many maximal left denominator sets (eg, this is the case if a ring h...

Safety, local and systemic immunomodulation, and tumor response to treatment with aerosolized natural interleukin 2 (nIL-2) applied five times a day were studied in a Phase I trial in 16 patients with pulmonary malignancies refractory to conventional therapy. The toxicity of inhaled nIL-2 was different from that observed after systemic administration. Reversible airway irritation causing a nonp...

Abstract Regarding the question of how idempotent elements affect reversible property rings, we study a version reversibility depending on idempotents. In this perspective, introduce right (resp., left )