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Idealiser rings of injective dimension one
No full textWe study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R.We study a certain type of prime Noetherian idealiser ring R of injective dimension 1, and prove for instance that the idempotent ideals of R are projective and that every non-zero projective ideal of R is uniquely of the form U E for some invertible ideal U and idempotent ideal E of R. Formulae are given for the number of idempotent ideals of R and the number of orders which contain R
Semi-prime Noetherian rings of injective dimension one
No full textLet R be a semi-prime Noetherian ring of injective dimension 1. Let P be a minimal prime ideal of R. In this paper it is shown that R/P need not have injective dimension 1. Necessary and sufficient conditions are given for R/P to have injective dimension 1.Let R be a semi-prime Noetherian ring of injective dimension 1. Let P be a minimal prime ideal of R. In this paper it is shown that R/P need not have injective dimension 1. Necessary and sufficient conditions are given for R/P to have injective dimension 1
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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