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Multisorted Tree Algebra

Received: 24 November 2014     Accepted: 5 December 2014     Published: 16 December 2014
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Abstract

This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations.

Published in Applied and Computational Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.acm.20140306.12
Page(s) 295-302
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Multisorted Algebra, Hierarchy, Aggregation, Abstract Data Type

References
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  • APA Style

    Erick Patrick Zobo, Marcel Fouda Ndjodo. (2014). Multisorted Tree Algebra. Applied and Computational Mathematics, 3(6), 295-302. https://doi.org/10.11648/j.acm.20140306.12

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    ACS Style

    Erick Patrick Zobo; Marcel Fouda Ndjodo. Multisorted Tree Algebra. Appl. Comput. Math. 2014, 3(6), 295-302. doi: 10.11648/j.acm.20140306.12

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    AMA Style

    Erick Patrick Zobo, Marcel Fouda Ndjodo. Multisorted Tree Algebra. Appl Comput Math. 2014;3(6):295-302. doi: 10.11648/j.acm.20140306.12

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  • @article{10.11648/j.acm.20140306.12,
      author = {Erick Patrick Zobo and Marcel Fouda Ndjodo},
      title = {Multisorted Tree Algebra},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {6},
      pages = {295-302},
      doi = {10.11648/j.acm.20140306.12},
      url = {https://doi.org/10.11648/j.acm.20140306.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.12},
      abstract = {This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations.},
     year = {2014}
    }
    

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    Y1  - 2014/12/16
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    AB  - This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations.
    VL  - 3
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Author Information
  • Department of Computer Sciences and Education Technologies (DITE), University of Yaounde I Yaounde, Cameroon

  • Department of Computer Sciences and Education Technologies (DITE), University of Yaounde I Yaounde, Cameroon

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