1 Ocak 2022 Dergi makalesi Açık Erişim

Aydogdu, Pinar; Durgun, Yilmaz

JSON

{
  "conceptrecid": "262162", 
  "created": "2023-07-29T15:46:39.130877+00:00", 
  "doi": "10.2989/16073606.2022.2109221", 
  "files": [
    {
      "bucket": "c7148490-0623-4e14-801a-68421df1c11b", 
      "checksum": "md5:2ebf1964c108b70cbc504d90d939b177", 
      "key": "bib-e3da95ea-d8c8-472c-9098-78c27a0b3d4e.txt", 
      "links": {
        "self": "https://aperta.ulakbim.gov.tr/api/files/c7148490-0623-4e14-801a-68421df1c11b/bib-e3da95ea-d8c8-472c-9098-78c27a0b3d4e.txt"
      }, 
      "size": 105, 
      "type": "txt"
    }
  ], 
  "id": 262163, 
  "links": {
    "badge": "https://aperta.ulakbim.gov.tr/badge/doi/10.2989/16073606.2022.2109221.svg", 
    "bucket": "https://aperta.ulakbim.gov.tr/api/files/c7148490-0623-4e14-801a-68421df1c11b", 
    "doi": "https://doi.org/10.2989/16073606.2022.2109221", 
    "html": "https://aperta.ulakbim.gov.tr/record/262163", 
    "latest": "https://aperta.ulakbim.gov.tr/api/records/262163", 
    "latest_html": "https://aperta.ulakbim.gov.tr/record/262163"
  }, 
  "metadata": {
    "access_right": "open", 
    "access_right_category": "success", 
    "communities": [
      {
        "id": "tubitak-destekli-proje-yayinlari"
      }
    ], 
    "creators": [
      {
        "affiliation": "Hacettepe Univ, Dept Math, Ankara, Turkey", 
        "name": "Aydogdu, Pinar"
      }, 
      {
        "affiliation": "Cukurova Univ, Dept Math, Adana, Turkey", 
        "name": "Durgun, Yilmaz"
      }
    ], 
    "description": "Proper classes (or exact structures) offer rich research topics due to their important role in category theory. Motivated by the studies on opposite of injective modules, we introduce a new approach to opposed to injectivity in terms of injectively generated proper classes. The smallest possible proper class generated injectively by a single module is the class of all split short exact sequences. We call a module M iota-indigent if the proper class injectively generated by M consists only of split short exact sequences. We are able to show that if R is a ring which is not von Neumann regular, then every right (pure-injective) R-module is either injective or iota-indigent if and only if R is an Artinian serial ring with J(2) (R) = 0 and has a unique non-injective simple right R-module up to isomorphism. Moreover, if R is a ring such that every simple right R-module is pure-injective, then every simple right R-module is t-indigent or injective if and only if R is either a right V-ring or R = A x B, where A is semisimple, and B is an Artinian serial ring with J(2) (B) = 0. We investigate the class iota(R) which consists of those proper classes P such that P is injectively generated by a module. We call such a class (right) proper injective profile of a ring R. We prove that if R is an Artinian serial ring with J(2) (R) = 0, then vertical bar iota(R)vertical bar = 2(n), where n is the number of non-isomorphic non-injective simple right R-modules. In addition, if iota(R) is a chain, then R is a right Noetherian ring over which every right R-module is either projective or i-test, and has a unique singular simple right R-module. Furthermore, in this case, R is either right hereditary or right Kasch. We observe that vertical bar iota(R)vertical bar not equal 3 for any ring R which is not von Neumann regular. We construct a bounded complete lattice structure on iota(R) in case iota(R) is a partially ordered set under set inclusion. Moreover, if R is an Artinian serial ring with J(2) (R) = 0, then this lattice structure is Boolean.", 
    "doi": "10.2989/16073606.2022.2109221", 
    "has_grant": false, 
    "journal": {
      "title": "QUAESTIONES MATHEMATICAE"
    }, 
    "license": {
      "id": "cc-by"
    }, 
    "publication_date": "2022-01-01", 
    "relations": {
      "version": [
        {
          "count": 1, 
          "index": 0, 
          "is_last": true, 
          "last_child": {
            "pid_type": "recid", 
            "pid_value": "262163"
          }, 
          "parent": {
            "pid_type": "recid", 
            "pid_value": "262162"
          }
        }
      ]
    }, 
    "resource_type": {
      "subtype": "article", 
      "title": "Dergi makalesi", 
      "type": "publication"
    }, 
    "science_branches": [
      "Di\u011fer"
    ], 
    "title": "THE OPPOSITE OF INJECTIVITY BY PROPER CLASSES"
  }, 
  "owners": [
    1
  ], 
  "revision": 1, 
  "stats": {
    "downloads": 4.0, 
    "unique_downloads": 4.0, 
    "unique_views": 18.0, 
    "version_downloads": 4.0, 
    "version_unique_downloads": 4.0, 
    "version_unique_views": 18.0, 
    "version_views": 19.0, 
    "version_volume": 420.0, 
    "views": 19.0, 
    "volume": 420.0
  }, 
  "updated": "2023-07-29T15:46:39.181983+00:00"
}