In [5] and [6], a nil clean ring was defined as a ring for which every element is the sum of a nilpotent and an idempotent. In this short article we characterize nil clean commutative group rings.

a group of 1,3-biarylhydrazide derivatives possessing a cox-2 azido pharmacophore at the para- position of the c-1 phenyl ring in conjunction with a n-3 phenyl or substituted-phenyl ring (4-f,4-cl,4-ome) were designed and synthesized based on nucleophilic substitution reaction. a molecular modelling study of these compounds showed that the designed molecules were well bound with the active site...

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

In the title compound, C(25)H(25)FN(4)OS, the thienopyrimidine fused-ring system is close to planar (r.m.s. deviation = 0.0089 Å), with a maximum deviation of 0.0261 (17) Å for the N atom adjacent to the benzene ring. This thienopyrimidine fused-ring system forms dihedral angles of 64.73 (3) and 81.56 (5)° with the adjacent benzyl and fluoro-phenyl rings, respectively. Inter-molecular N-H⋯F and...

The central pyrazole ring in the title compound, C17H16FN3S, adopts an envelope conformation with the methine C atom bearing the 4-fluoro-phenyl substituent as the flap atom. Whereas the tolyl ring is slightly twisted out of the least-squares plane through the pyrazole ring [dihedral angle = 13.51 (11)°], the fluoro-benzene ring is almost perpendicular [dihedral angle = 80.21 (11)°]. The thio-a...

Let R be an associative ring with identity, C(R) denote the center of R, and g(x) be a polynomial in the polynomial ring C(R)[x]. R is called strongly g(x)-clean if every element r ∈ R can be written as r = s+u with g(s) = 0, u a unit of R, and su = us. The relation between strongly g(x)-clean rings and strongly clean rings is determined, some general properties of strongly g(x)-clean rings are...

The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras rings using some functional identities. Let A be a unital semiprime algebra let F,G : ? linear mappings satisfying F(x) =-x2G(x-1) for all x Inv(A), where Inv(A) denotes the set invertible elements A. Then both F G are Another result in regard as follows. n > 1 ...

Equatorial/axial conversion in piperidine and phosphorinane with different substituents wereinvestigated with great details. Three possible routes, i.e. heteroatom inversion and two ring inversiontype were considered. Ring conversion can occur via two pathways one starts with ring flatteningfrom the heteroatom site (nitrogen in piperidine and phosphorous in phosphorinane) and the otherinitiates...

This paper mainly focuses on permutation polynomials over the residue class ring ZN , where N > 3 is composite. We have proved that for the polynomial f(x) = a1x 1 + · · · + akx with integral coefficients, f(x) mod N permutes ZN if and only if f(x) mod N permutes Sμ for all μ | N , where Sμ = {0 < t < N : gcd(N, t) = μ} and SN = S0 = {0}. Based on it, we give a lower bound of the differential u...

Let A be the polynomial ring over k (a field of characteristic zero) in n + 1 variables. The commuting derivations conjecture states that n commuting locally nilpotent derivations on A, linearly independent over A, must satisfy A D 1 ,...,Dm = k[f ] where f is a coordinate. The conjecture can be formulated as stating that a (G m) n-action on k n+1 must have invariant ring k[f ] where f is a coo...