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.

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

We completely determine those natural numbers $n$ for which the full matrix ring $M_n(F_2)$ and triangular $T_n(F_2)$ over two elements field $F_2$ are either n-torsion clean or almost clean, respectively. These results somewhat address settle a question, recently posed by Danchev-Matczuk in Contemp. Math. (2019) as well they supply more precise aspect nil-cleanness property of $n\times n$ all ...

Let R be a commutative ring with multiplicative identity and C coassociative counital R-coalgebra the α-condition. A clean comodules defined based on cleanness rings modules. C-comodule M is comodule if endomorphism of clean. over itself i.e., as For an idempotent e ∈ R, there are relations between eRe R. It’s motivated us to investigate this condition for coalgebra. any C, we can construct ⇀C↼...

Air exhibiting very low concentrations of light-scattering aerosol particles is occasionally observed even in industrialized regions. Evidence is presented that this very clean air results from highly efficient removal of aerosol particles coupled to the removal of water in precipitation.

We analyze the crossover from an hc /e periodicity of the persistent current in flux-threaded clean metallic rings toward an hc /2e-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the hc /e versus the hc /2e periodic components of the current density....

We redefine the uniqueness type system of the functional programming language Clean for the lambda calculus. Our treatment of curried functions is very different from their treatment in Clean, resulting in a much simpler type system (for example, the subtyping relation in Clean is no longer necessary). Further, our system supports arbitrary rank types, which has the additional benefit that we c...

The Cox construction presents a toric variety as quotient of affine space by torus. category coherent sheaves on the corresponding stack thus has an evident description invariants in modules over polynomial ring. Here we give mirror to this description, and particular, clean new proof symmetry for smooth stacks.