in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

In this note, we introduce the concept of semi-*-IFP, involutive version semi-IFP, which is a generalization quasi-*-IFP and *-reducedness *-rings. We study basic structure properties *-rings having semi-*-IFP give results for IFPs in rings with involution. Several counterexamples are stated to connect versions IFP. discuss conditions be extended into *-subrings ring upper triangular matrices. ...

Donor-acceptor [2]catenanes based on cyclobis(paraquat-p-phenylene) as the pi-acceptor ring have been used prominently in the construction of functional molecular devices. We report here their thermodynamically controlled synthesis from isolated pi-donor and pi-acceptor rings under the catalytic influence of tetra butylammonium iodide. The initial nucleophilic attack of iodide ion, which opens ...

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.

The synthesis of a functionally rigid [2]rotaxane incorporating pi-electron rich 1,5-disubstituted naphthalene (NP) ring systems, encircled by the pi-electron deficient tetracationic cyclophane, cyclobis(paraquat-p-phenylene), is described; in the solid state, the molecules of this donor-acceptor [2]rotaxane line themselves up in parallel pi-pi stacks of alternating NP ring systems and bipyridi...

It is shown that if the ring of constants of a restricted differential Lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.