1,721,003 research outputs found
Classical localizability in solvable enveloping algebras and Poincaré-Birkhoff-Witt extensions
No full textAbstractIn several classes of noncommutative noetherian rings, Jategaonkar's intersection conditions are verified for finite unions of cliques of prime ideals, and it follows that these finite unions of cliques are classically localizable if they satisfy incomparability. Among the rings in question are the enveloping algebra of any finite-dimensional solvable Lie algebra g over any field k of characteristic zero, any twisted smash product R # U(g) where R is a commutative noetherian k-algebra and g acts on R via k-linear derivations, and certain iterated differential operator rings over R. In contrast to previously verified cases, k is allowed to be countable. One tool used here—a lying over theorem for cliques—has some independent interest. Namely, if R ⊆ S is a flat finite centralizing extension of noetherian rings satisfying the second layer condition, and if X is a clique in Spec(R), there exists a clique Y in Spec(S) such that {P ∩ R|P ϵ Y} = X
Rank functions and K0 of regular rings
No full textAbstractThis paper is concerned with the existence and uniqueness of rank and pseudo-rank functions on a von Neumann regular ring R. The main technique used involves transferring hypotheses becomes a partially ordered abelian group. It is shown that the existence of a pseudo-rank function on R is equivalent to certain finiteness conditions on the matrix rings over R. As a corollary, necessary and sufficient conditions are obtained for the existence of a rank function on a simple regular ring. Uniqueness of a rank function is shown to be equivalent to certain comparability conditions on the principal right ideals of R. Other results concern the existence of enough pseudo-rank functions to distinguish nonzero ring elements from zero, or to distinguish between non-isomorphic principal right ideals.All rings in this paper are associative with unit (but usually noncommutative), and all modules are unital right modules. We use “regular” to mean “von Neumann regular”.The research of the first author was partially supported by National Science Foundation Grant No. GP-43029
Prime ideals in skew polynomial rings and quantized Weyl algebras
No full textThe concern of this paper is to investigate the structure of skew polynomial rings (Ore extensions) of the form T=R[θ; σ, δ] where σ and δ are both nontrivial, and in particular to analyze the prime ideals of T. The main focus is on the case that R is commutative noetherian. In this case, the prime ideals of T are classified, polynomial identities and Artin-Rees separation in prime factor rings are investigated, and cliques of prime ideals are studied. The second layer condition is proved, as well as boundedness of uniform ranks for the prime factor rings corresponding to any clique. Futher, q-skew derivations on noncommutative coefficient rings are introduced, and some preliminary results on contractions of prime ideals of T are obtained in this setting. Finally, prime ideals in quantized Weyl algebras over fields are analyzed
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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