From lattices to Hv-matrices
In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2016-11-01
|
| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/auom-2016-0055 |
| _version_ | 1811329817168052224 |
|---|---|
| author | Křehlík Štěpán Novák Michal |
| author_facet | Křehlík Štěpán Novák Michal |
| author_sort | Křehlík Štěpán |
| collection | DOAJ |
| description | In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures. |
| first_indexed | 2024-04-13T15:50:37Z |
| format | Article |
| id | doaj.art-2e409f4ba5a843cb9bd40b66e42df27c |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-13T15:50:37Z |
| publishDate | 2016-11-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-2e409f4ba5a843cb9bd40b66e42df27c2022-12-22T02:40:50ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352016-11-0124320922210.1515/auom-2016-0055From lattices to Hv-matricesKřehlík Štěpán0Novák Michal1Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech RepublicIn this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.https://doi.org/10.1515/auom-2016-0055distributive latticehv-matrixhv-ringjoin spacepartially ordered semigroup.primary 20n20secondary 15b3306e9906d75 |
| spellingShingle | Křehlík Štěpán Novák Michal From lattices to Hv-matrices Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica distributive lattice hv-matrix hv-ring join space partially ordered semigroup. primary 20n20 secondary 15b33 06e99 06d75 |
| title | From lattices to Hv-matrices |
| title_full | From lattices to Hv-matrices |
| title_fullStr | From lattices to Hv-matrices |
| title_full_unstemmed | From lattices to Hv-matrices |
| title_short | From lattices to Hv-matrices |
| title_sort | from lattices to hv matrices |
| topic | distributive lattice hv-matrix hv-ring join space partially ordered semigroup. primary 20n20 secondary 15b33 06e99 06d75 |
| url | https://doi.org/10.1515/auom-2016-0055 |
| work_keys_str_mv | AT krehlikstepan fromlatticestohvmatrices AT novakmichal fromlatticestohvmatrices |