Annihilator conditions on polynomials. II.
The present authors have already published several papers, too numerous to list here, some in collaboration with others, on annihilator conditions on polynomials and various types of Baer conditions on rings and near-rings. To describe the many results in this paper in detail would require a lot of space, so we will just give a flavour. A Baer ring is a ring with unity such that the right annihilator of every nonempty subset is generated as a right ideal by an idempotent. As often happens, the transfer of this definition and related ones to near-rings leads to several possibilities. Given a ring \(R\), the relationship between the Baer type properties of \(R\) and \(R[x]\) have been studied in part I [the authors, Commun. Algebra 29, No. 5, 2097--2112 (2001; Zbl 0990.16033)]. This has been taken further in this work by considering the situation in left near-rings \(N\) and the relationship between the various properties in a ring \(R\) and the near-ring \(R[x]\) of polynomials over \(R\), where the operations in \(R[x]\) are the usual addition and substitution. Several results linking the properties of the ring \(R\) and the near-ring \(R[x]\) are obtained, many similar to earlier ring results although the structure of \(R[x]\) arises from a very different operation to that in the ring of polynomials. There are also examples to show the limits of the results. There is much of interest here.
scientific article; zbMATH DE number 2111512