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Generalized derivations and multilinear polynomials in prime rings
No full textLet R be a prime ring with Utumi quotient ring U and extended centroid C, g a nonzero generalized derivation of R, I a nonzero right ideal of R, f (r1,...,rk) a multilinear polynomial over C and n ? 2 be a fixed integer. If g( f (r1,...,rk)n) = g( f (r1,...,rk))n for all r1,...,rk ? I, then one of the following holds: (1) IC = eRC for some idempotent e ? soc(RC) and f (x1,...,xk) is central-valued on eRCe(2) there exist a,b ? U such that g(x) = ax+xb for all x ? R and (a-?)I = (0), (b-?)I = (0) for some ?,? ? C with (a +b)n-1 = 1(3) there exists a ? U such that g(x) = ax for all x ? R with aI = (0)
Generalized Derivations Acting on Multilinear Polynomials in Prime Rings and Banach Algebras
No full textLet R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, F and G, the two nonzero generalized derivations of R, I an ideal of R and f(x(1),..., x(n)) a multilinear polynomial over C which is not central valued on R. If F(G(f (x(1),..., x(n))) f (x(1),..., x(n))) = 0 for all x(1),..., x(n). I, then one of the followings holds: (1) there exist a, b epsilon U such that F(x) = ax and G(x) = bx for all x. R with ab = 0; (2) there exist a, b, p epsilon U such that F(x) = ax + xb and G(x) = px for all x epsilon R with F(p) = 0 and f (x(1),..., x(n))(2) is central valued on R. We also obtain some related results in cases where R is a semiprime ring and Banach algebra.INSA, India; TUBA, TurkeyTurkish Academy of SciencesThe authors would like to thank the referee for providing shortened proof of Lemma 2.1 in the paper. This work was done when the first author visited Ege University, TURKEY, from the 9th June 2014 to the 15th June 2014 under the INSA-TUBA Exchange of Scientists Programme. The first author is grateful to INSA, India and TUBA, Turkey for the financial support provided for this visit
Generalized Derivations With Left Annihilator Conditions in Prime and Semiprime Rings
No full textLet R be a prime ring with its Utumi ring of quotients U, C = Z(U) be the extended centroid of R, H and G two generalized derivations of R, L a noncentral Lie ideal of R, I a nonzero ideal of R. The left annihilator of S ⊆ R is denoted by lR(S) and defined by lR(S) = {x ∈ R| xS = 0}. Suppose that S = {H(un)un +unG(un) | u ∈ L} and T = {H(xn)xn +xnG(xn) | x ∈ I}, where n ≥ 1 is a fixed integer. In the paper, we investigate the cases when the sets lR(S) and lR(T ) are nonzero
Generalized derivations acting on multilinear polynomials in prime rings
Get PDFsummary:Let be a noncommutative prime ring of characteristic different from with Utumi quotient ring and extended centroid , let , and be three generalized derivations of , an ideal of and a multilinear polynomial over which is not central valued on . If for all , then one of the following conditions holds: \item {(1)} there exist and such that , and for all ; \item {(2)} there exist such that , and for all , with ; \item {(3)} there exist and such that , and for all ; \item {(4)} is central valued on and one of the following conditions holds: \itemitem {(a)} there exist such that , and for all , with ; \itemitem {(b)} there exist such that , and for all , with
A note on generalized skew-derivations on multilinear polynomials in prime rings
No full textLet R be a prime ring of characteristic different from 2, Qr its rightMartindale quotient ring and C its extended centroid, f(X1; : : : ;Xn) a multilinearpolynomial over C that is noncentral-valued on R and F a generalized skew derivationof R. If for some 0 ≠ a ∈R-C, a[F(f(r)); f(r)] - [F(f(r)); f(r)]α ∈ Z(R)for all r = (r1; : : : ; rn) ∈ Rn then one of the following conditions holds:(1) there exists λ, ∈ C such that F(x) = λx for all x ∈ R;(2) there exist b ∈ Qr and λ ∈ C such that F(x) = bx + xb + λx for all x ∈ R andf(X1; : : : ;Xn)2 is central valued on R.
As an application of this result, we investigate the commutator [S; T] ∈ Z(R), whereS = {[F(u); u]lu ∈ f(R)} and T = f[G(v); v]jv ∈ f(R)}, F and G two generalizedskew derivations of R.
Key words: Prime ring, derivation, generalized derivation, generalized skew derivation,extended centroid
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
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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