On Bernstein Algebras of n-th Order View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1994

AUTHORS

S. Gonzalez , J. C. Gutierrez , C. Martinez

ABSTRACT

Let (A,w) be a finite dimensional n-th order Bernstein algebra over an infinite field K (charK ≠ 2). If e ∈ A is a nontrivial idempotent then A = Ke ⊕ Ue ⊕ Ve where and Ve = {x ∈ Kerw/Renx = 0}. In this paper we show the following results:(1) The dimension of Ue does not depend on idempotent e,(2) if K = ℝ and dimUe = r then there is an r-parametric family of idempotents of the A, (3) if K = ℝ then dimRVe ≥ n. More... »

PAGES

158-163

Book

TITLE

Non-Associative Algebra and Its Applications

ISBN

978-94-010-4429-5
978-94-011-0990-1

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-011-0990-1_25

DOI

http://dx.doi.org/10.1007/978-94-011-0990-1_25

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028285929


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Oviedo", 
          "id": "https://www.grid.ac/institutes/grid.10863.3c", 
          "name": [
            "Departamento de Matem\u00e1ticas, Universidad de Oviedo, 33007, Oviedo, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Gonzalez", 
        "givenName": "S.", 
        "id": "sg:person.016661036521.95", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016661036521.95"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Oviedo", 
          "id": "https://www.grid.ac/institutes/grid.10863.3c", 
          "name": [
            "Departamento de Matem\u00e1ticas, Universidad de Oviedo, 33007, Oviedo, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Gutierrez", 
        "givenName": "J. C.", 
        "id": "sg:person.07555436243.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07555436243.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Oviedo", 
          "id": "https://www.grid.ac/institutes/grid.10863.3c", 
          "name": [
            "Departamento de Matem\u00e1ticas, Universidad de Oviedo, 33007, Oviedo, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Martinez", 
        "givenName": "C.", 
        "id": "sg:person.015261576461.61", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015261576461.61"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1112/plms/s3-40.2.346", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002335212"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/jlms/s2-9.4.613", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044990209"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imammb/7.1.33", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059688141"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1994", 
    "datePublishedReg": "1994-01-01", 
    "description": "Let (A,w) be a finite dimensional n-th order Bernstein algebra over an infinite field K (charK \u2260 2). If e \u2208 A is a nontrivial idempotent then A = Ke \u2295 Ue \u2295 Ve where and Ve = {x \u2208 Kerw/Renx = 0}. In this paper we show the following results:(1) The dimension of Ue does not depend on idempotent e,(2) if K = \u211d and dimUe = r then there is an r-parametric family of idempotents of the A, (3) if K = \u211d then dimRVe \u2265 n.", 
    "editor": [
      {
        "familyName": "Gonz\u00e1lez", 
        "givenName": "Santos", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-94-011-0990-1_25", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-94-010-4429-5", 
        "978-94-011-0990-1"
      ], 
      "name": "Non-Associative Algebra and Its Applications", 
      "type": "Book"
    }, 
    "name": "On Bernstein Algebras of n-th Order", 
    "pagination": "158-163", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1028285929"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-94-011-0990-1_25"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "86bf8f9fa8f99c2ebef65837359cab68dd2d502ddaab15c052860f95d9649638"
        ]
      }
    ], 
    "publisher": {
      "location": "Dordrecht", 
      "name": "Springer Netherlands", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-94-011-0990-1_25", 
      "https://app.dimensions.ai/details/publication/pub.1028285929"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T09:28", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000372_0000000372/records_117109_00000001.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-94-011-0990-1_25"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-0990-1_25'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-0990-1_25'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-0990-1_25'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-0990-1_25'


 

This table displays all metadata directly associated to this object as RDF triples.

88 TRIPLES      23 PREDICATES      30 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-94-011-0990-1_25 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Ndc96f9b32fd646a5860df86e87391dfa
4 schema:citation https://doi.org/10.1093/imammb/7.1.33
5 https://doi.org/10.1112/jlms/s2-9.4.613
6 https://doi.org/10.1112/plms/s3-40.2.346
7 schema:datePublished 1994
8 schema:datePublishedReg 1994-01-01
9 schema:description Let (A,w) be a finite dimensional n-th order Bernstein algebra over an infinite field K (charK ≠ 2). If e ∈ A is a nontrivial idempotent then A = Ke ⊕ Ue ⊕ Ve where and Ve = {x ∈ Kerw/Renx = 0}. In this paper we show the following results:(1) The dimension of Ue does not depend on idempotent e,(2) if K = ℝ and dimUe = r then there is an r-parametric family of idempotents of the A, (3) if K = ℝ then dimRVe ≥ n.
10 schema:editor Neaebc57352d84163822441a436ea0c00
11 schema:genre chapter
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf N61d51cad91ce4c87b173196dbc32ca1f
15 schema:name On Bernstein Algebras of n-th Order
16 schema:pagination 158-163
17 schema:productId N044a3e9457564386996346d6c02886bc
18 N1b488286abe14da6af6d1d36ef4ee740
19 Neeff885e10d445b0b3b613f9a2e3b0ee
20 schema:publisher Nc1c88e00158446f3b66130a25d02a495
21 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028285929
22 https://doi.org/10.1007/978-94-011-0990-1_25
23 schema:sdDatePublished 2019-04-16T09:28
24 schema:sdLicense https://scigraph.springernature.com/explorer/license/
25 schema:sdPublisher N396cb2c637f747c08d64053cde586c48
26 schema:url https://link.springer.com/10.1007%2F978-94-011-0990-1_25
27 sgo:license sg:explorer/license/
28 sgo:sdDataset chapters
29 rdf:type schema:Chapter
30 N044a3e9457564386996346d6c02886bc schema:name readcube_id
31 schema:value 86bf8f9fa8f99c2ebef65837359cab68dd2d502ddaab15c052860f95d9649638
32 rdf:type schema:PropertyValue
33 N15acc1bb2fd64a6ba1e6ca92f77c2e33 rdf:first sg:person.015261576461.61
34 rdf:rest rdf:nil
35 N1b488286abe14da6af6d1d36ef4ee740 schema:name dimensions_id
36 schema:value pub.1028285929
37 rdf:type schema:PropertyValue
38 N2323fb5188474aa3822bf0003e1a28c3 schema:familyName González
39 schema:givenName Santos
40 rdf:type schema:Person
41 N396cb2c637f747c08d64053cde586c48 schema:name Springer Nature - SN SciGraph project
42 rdf:type schema:Organization
43 N5684e8ce8b6747e794f8fec85f0125cf rdf:first sg:person.07555436243.48
44 rdf:rest N15acc1bb2fd64a6ba1e6ca92f77c2e33
45 N61d51cad91ce4c87b173196dbc32ca1f schema:isbn 978-94-010-4429-5
46 978-94-011-0990-1
47 schema:name Non-Associative Algebra and Its Applications
48 rdf:type schema:Book
49 Nc1c88e00158446f3b66130a25d02a495 schema:location Dordrecht
50 schema:name Springer Netherlands
51 rdf:type schema:Organisation
52 Ndc96f9b32fd646a5860df86e87391dfa rdf:first sg:person.016661036521.95
53 rdf:rest N5684e8ce8b6747e794f8fec85f0125cf
54 Neaebc57352d84163822441a436ea0c00 rdf:first N2323fb5188474aa3822bf0003e1a28c3
55 rdf:rest rdf:nil
56 Neeff885e10d445b0b3b613f9a2e3b0ee schema:name doi
57 schema:value 10.1007/978-94-011-0990-1_25
58 rdf:type schema:PropertyValue
59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
60 schema:name Mathematical Sciences
61 rdf:type schema:DefinedTerm
62 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
63 schema:name Pure Mathematics
64 rdf:type schema:DefinedTerm
65 sg:person.015261576461.61 schema:affiliation https://www.grid.ac/institutes/grid.10863.3c
66 schema:familyName Martinez
67 schema:givenName C.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015261576461.61
69 rdf:type schema:Person
70 sg:person.016661036521.95 schema:affiliation https://www.grid.ac/institutes/grid.10863.3c
71 schema:familyName Gonzalez
72 schema:givenName S.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016661036521.95
74 rdf:type schema:Person
75 sg:person.07555436243.48 schema:affiliation https://www.grid.ac/institutes/grid.10863.3c
76 schema:familyName Gutierrez
77 schema:givenName J. C.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07555436243.48
79 rdf:type schema:Person
80 https://doi.org/10.1093/imammb/7.1.33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059688141
81 rdf:type schema:CreativeWork
82 https://doi.org/10.1112/jlms/s2-9.4.613 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044990209
83 rdf:type schema:CreativeWork
84 https://doi.org/10.1112/plms/s3-40.2.346 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002335212
85 rdf:type schema:CreativeWork
86 https://www.grid.ac/institutes/grid.10863.3c schema:alternateName University of Oviedo
87 schema:name Departamento de Matemáticas, Universidad de Oviedo, 33007, Oviedo, Spain
88 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...