Bibliometric counting methods need to be validated against perceived notions of authorship credit allocation, and standardized
by rejecting methods with poor fit or questionable ethical implications. Harmonic counting meets these concerns by exhibiting
a robust fit to previously published empirical data from medicine, psychology and chemistry, and by complying with three basic
ethical criteria for the equitable sharing of authorship credit. Harmonic counting can also incorporate additional byline
information about equal contribution, or the elevated status of a corresponding last author. By contrast, several previously
proposed counting schemes from the bibliometric literature including arithmetic, geometric and fractional counting, do not
fit the empirical data as well and do not consistently meet the ethical criteria. In conclusion, harmonic counting would seem
to provide unrivalled accuracy, fairness and flexibility to the long overdue task of standardizing bibliometric allocation
of publication and citation credit.
A collection of coauthored papers is the new norm for doctoral dissertations in the natural and biomedical sciences, yet there
is no consensus on how to partition authorship credit between PhD candidates and their coauthors. Guidelines for PhD programs
vary but tend to specify only a suggested range for the number of papers to be submitted for evaluation, sometimes supplemented
with a requirement for the PhD candidate to be the principal author on the majority of submitted papers. Here I use harmonic
counting to quantify the actual amount of authorship credit attributable to individual PhD graduates from two Scandinavian
universities in 2008. Harmonic counting corrects for the inherent inflationary and equalizing biases of routine counting methods,
thereby allowing the bibliometrically identifiable amount of authorship credit in approved dissertations to be analyzed with
unprecedented accuracy. Unbiased partitioning of authorship credit between graduates and their coauthors provides a post hoc
bibliometric measure of current PhD requirements, and sets a de facto baseline for the requisite scientific productivity of
these contemporary PhD’s at a median value of approximately 1.6 undivided papers per dissertation. Comparison with previous
census data suggests that the baseline has shifted over the past two decades as a result of a decrease in the number of submitted
papers per candidate and an increase in the number of coauthors per paper. A simple solution to this shifting baseline syndrome
would be to benchmark the amount of unbiased authorship credit deemed necessary for successful completion of a specific PhD
program, and then monitor for departures from this level over time. Harmonic partitioning of authorship credit also facilitates
cross-disciplinary and inter-institutional analysis of the scientific output from different PhD programs. Juxtaposing bibliometric
benchmarks with current baselines may thus assist the development of harmonized guidelines and transparent transnational quality
assurance procedures for doctoral programs by providing a robust and meaningful standard for further exploration of the causes
of intra- and inter-institutional variation in the amount of unbiased authorship credit per dissertation.
We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that nil-McCoy rings need not be right linearly McCoy. More examples of nil-McCoy rings are given by various extensions. On the other hand, the properties of α-McCoy rings by considering the polynomials in the skew polynomial ring R[x; α] in place of the ring R[x] are also investigated. For a monomorphism α of a ring R, it is shown that if R is weak α-rigid and α-reversible then R is α-McCoy.
Authors:Ebrahim Hashemi, Fatemeh Shokuhifar, and Abdollah Alhevaz
The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.