FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W153882652> ?p ?o ?g. }

• W153882652 abstract "We investigate certain classes of modules of low projective dimension over polynomial rings whose free resolutions have known special structure. We begin with projective modules and investigate a computational approach to a famous theorem of Quillen-Suslin, which states that every finitely generated projective module over S = R[x 1,...,xn], with R a principal ideal domain, is free. We describe a package for the computer algebra system Macaulay2 which we have developed to compute free generating sets for projective modules. We give special attention to the algorithms when R is the ring of integers and provide a constructive proof of a result of Suslin-Vaserstein, for which we could not find a constructive proof in the literature. The approach to this proof involves the ideas of strong Grobner bases for ideals of polynomials with integral coefficients and “leading coefficient ideals.'' Moving to projective dimension two, we fix the ring B = k[x,y], with k a field, and consider homogeneous height two perfect ideals I = (g1,g2, g3) generated by homogeneous forms gi with deg gi = di. Motivated by work of Cox-Kustin-Polini-Ulrich, we study the problem of constructing a local inverse to a particular morphism Φ which sends a 3 × 2 matrix of homogeneous forms of B to a triple of its signed 2 × 2 minors. For each possibility for the graded Betti numbers of B /I we describe an open cover of the parameter space of coefficients of the generators, and on each open set we describe the precise relationship between the coefficients of the forms gi and the coefficients of the forms appearing in a presentation matrix p such that Φ(p) = (g1,g 2,g3). Furthermore, in the case where the degrees of each of the columns of p are the same, we generalize results of [CKPU] on the existence of universal projective resolutions for algebras B/I whose graded Betti numbers satisfy certain conditions. In projective dimension three, we fix the ring B = k[x,y,z], with k a field, and consider homogeneous grade three Gorenstein ideals I ⊆ B. The Buchsbaum-Eisenbud structure theorem for grade three Gorenstein algebras such as B/I implies that there exists an alternating presentation matrix ψ. In a recent paper, Fisher describes how to produce such an alternating presentation matrix in the case when I is generated in a single degree. We extend this result and provide an algorithm to compute an alternating presentation matrix when I has generators in any degrees." @default.
• W153882652 created "2016-06-24" @default.
• W153882652 creator A5010622972 @default.
• W153882652 creator A5059882312 @default.
• W153882652 date "2012-01-01" @default.
• W153882652 modified "2023-09-23" @default.
• W153882652 title "A computational approach to the quillen-suslin theorem, buchsbaum-eisenbud matrices, and generic hilbert-burch matrices" @default.
• W153882652 hasPublicationYear "2012" @default.
• W153882652 type Work @default.
• W153882652 sameAs 153882652 @default.
• W153882652 citedByCount "0" @default.
• W153882652 crossrefType "journal-article" @default.
• W153882652 hasAuthorship W153882652A5010622972 @default.
• W153882652 hasAuthorship W153882652A5059882312 @default.
• W153882652 hasConcept C118615104 @default.
• W153882652 hasConcept C129621563 @default.
• W153882652 hasConcept C134306372 @default.
• W153882652 hasConcept C136119220 @default.
• W153882652 hasConcept C137212723 @default.
• W153882652 hasConcept C177846678 @default.
• W153882652 hasConcept C202444582 @default.
• W153882652 hasConcept C33676613 @default.
• W153882652 hasConcept C33923547 @default.
• W153882652 hasConcept C75280867 @default.
• W153882652 hasConcept C90119067 @default.
• W153882652 hasConcept C9485509 @default.
• W153882652 hasConceptScore W153882652C118615104 @default.
• W153882652 hasConceptScore W153882652C129621563 @default.
• W153882652 hasConceptScore W153882652C134306372 @default.
• W153882652 hasConceptScore W153882652C136119220 @default.
• W153882652 hasConceptScore W153882652C137212723 @default.
• W153882652 hasConceptScore W153882652C177846678 @default.
• W153882652 hasConceptScore W153882652C202444582 @default.
• W153882652 hasConceptScore W153882652C33676613 @default.
• W153882652 hasConceptScore W153882652C33923547 @default.
• W153882652 hasConceptScore W153882652C75280867 @default.
• W153882652 hasConceptScore W153882652C90119067 @default.
• W153882652 hasConceptScore W153882652C9485509 @default.
• W153882652 hasLocation W1538826521 @default.
• W153882652 hasOpenAccess W153882652 @default.
• W153882652 hasPrimaryLocation W1538826521 @default.
• W153882652 hasRelatedWork W1489090944 @default.
• W153882652 hasRelatedWork W1684637434 @default.
• W153882652 hasRelatedWork W1976931624 @default.
• W153882652 hasRelatedWork W2011876675 @default.
• W153882652 hasRelatedWork W2018972757 @default.
• W153882652 hasRelatedWork W2046648680 @default.
• W153882652 hasRelatedWork W2088764508 @default.
• W153882652 hasRelatedWork W2094976779 @default.
• W153882652 hasRelatedWork W2118890583 @default.
• W153882652 hasRelatedWork W2132830567 @default.
• W153882652 hasRelatedWork W2137145679 @default.
• W153882652 hasRelatedWork W2139317558 @default.
• W153882652 hasRelatedWork W2187151428 @default.
• W153882652 hasRelatedWork W3014785580 @default.
• W153882652 hasRelatedWork W3102923577 @default.
• W153882652 hasRelatedWork W3112157416 @default.
• W153882652 hasRelatedWork W3157012912 @default.
• W153882652 hasRelatedWork W3201118933 @default.
• W153882652 hasRelatedWork W84772786 @default.
• W153882652 hasRelatedWork W998356090 @default.
• W153882652 isParatext "false" @default.
• W153882652 isRetracted "false" @default.
• W153882652 magId "153882652" @default.
• W153882652 workType "article" @default.