Imbrication algebras -- algebraic structures of nesting order
This paper is about ``imbrication algebras'', universal algebras with one binary operator in their signature, the operator for formation of ordered pairs, called here ``pairing operator'', and with the ``characteristic property of ordered pairs'' as their sole axiom. Th...
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2018-11-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v26-n3/v26-n3-(pp233-250).pdf |
| _version_ | 1811279760607674368 |
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| author | Ioachim M. Drugus Volodymyr G. Skobelev |
| author_facet | Ioachim M. Drugus Volodymyr G. Skobelev |
| author_sort | Ioachim M. Drugus |
| collection | DOAJ |
| description | This paper is about ``imbrication algebras'', universal algebras with one binary operator in their signature, the operator for formation of ordered pairs, called here ``pairing operator'', and with the ``characteristic property of ordered pairs'' as their sole axiom. These algebras have been earlier introduced by the first author as reducts of ``aggregate algebras'', universal algebras proposed as models for a set theory convenient for formalization of data structures. The term ``aggregate'' is used to generalize three fundamental notions of set theory: set, atom and ordered pair. Thus, this paper initiates the research of aggregate algebras by narrowing the focus to one type of their main reducts -- the reduct which deals with ordered pairs. |
| first_indexed | 2024-04-13T01:01:34Z |
| format | Article |
| id | doaj.art-f4f4cf05e9ca49a9bcae912d7fe964e2 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-13T01:01:34Z |
| publishDate | 2018-11-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-f4f4cf05e9ca49a9bcae912d7fe964e22022-12-22T03:09:28ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422018-11-01263(78)233250Imbrication algebras -- algebraic structures of nesting orderIoachim M. Drugus0Volodymyr G. Skobelev1Institute of Mathematics and Computer Science, 5 Academiei str., MD-2028, Chisinau, Republic of MoldovaV.M. Glushkov Institute of Cybernetics of NAS of Ukraine, 40 Glushkova ave., Kyiv, Ukraine, 03187This paper is about ``imbrication algebras'', universal algebras with one binary operator in their signature, the operator for formation of ordered pairs, called here ``pairing operator'', and with the ``characteristic property of ordered pairs'' as their sole axiom. These algebras have been earlier introduced by the first author as reducts of ``aggregate algebras'', universal algebras proposed as models for a set theory convenient for formalization of data structures. The term ``aggregate'' is used to generalize three fundamental notions of set theory: set, atom and ordered pair. Thus, this paper initiates the research of aggregate algebras by narrowing the focus to one type of their main reducts -- the reduct which deals with ordered pairs.http://www.math.md/files/csjm/v26-n3/v26-n3-(pp233-250).pdfcancellative magmaCatalan numberMerkle treeordered pairquasi-variety |
| spellingShingle | Ioachim M. Drugus Volodymyr G. Skobelev Imbrication algebras -- algebraic structures of nesting order Computer Science Journal of Moldova cancellative magma Catalan number Merkle tree ordered pair quasi-variety |
| title | Imbrication algebras -- algebraic structures of nesting order |
| title_full | Imbrication algebras -- algebraic structures of nesting order |
| title_fullStr | Imbrication algebras -- algebraic structures of nesting order |
| title_full_unstemmed | Imbrication algebras -- algebraic structures of nesting order |
| title_short | Imbrication algebras -- algebraic structures of nesting order |
| title_sort | imbrication algebras algebraic structures of nesting order |
| topic | cancellative magma Catalan number Merkle tree ordered pair quasi-variety |
| url | http://www.math.md/files/csjm/v26-n3/v26-n3-(pp233-250).pdf |
| work_keys_str_mv | AT ioachimmdrugus imbricationalgebrasalgebraicstructuresofnestingorder AT volodymyrgskobelev imbricationalgebrasalgebraicstructuresofnestingorder |