The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier.
Published in | Pure and Applied Mathematics Journal (Volume 6, Issue 4) |
DOI | 10.11648/j.pamj.20170604.12 |
Page(s) | 114-119 |
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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. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Function Algebra, Relation Algebra, Universal Post Algebra
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APA Style
Maydim Malkov. (2017). Galois and Post Algebras of Compositions (Superpositions). Pure and Applied Mathematics Journal, 6(4), 114-119. https://doi.org/10.11648/j.pamj.20170604.12
ACS Style
Maydim Malkov. Galois and Post Algebras of Compositions (Superpositions). Pure Appl. Math. J. 2017, 6(4), 114-119. doi: 10.11648/j.pamj.20170604.12
AMA Style
Maydim Malkov. Galois and Post Algebras of Compositions (Superpositions). Pure Appl Math J. 2017;6(4):114-119. doi: 10.11648/j.pamj.20170604.12
@article{10.11648/j.pamj.20170604.12, author = {Maydim Malkov}, title = {Galois and Post Algebras of Compositions (Superpositions)}, journal = {Pure and Applied Mathematics Journal}, volume = {6}, number = {4}, pages = {114-119}, doi = {10.11648/j.pamj.20170604.12}, url = {https://doi.org/10.11648/j.pamj.20170604.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170604.12}, abstract = {The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier.}, year = {2017} }
TY - JOUR T1 - Galois and Post Algebras of Compositions (Superpositions) AU - Maydim Malkov Y1 - 2017/07/20 PY - 2017 N1 - https://doi.org/10.11648/j.pamj.20170604.12 DO - 10.11648/j.pamj.20170604.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 114 EP - 119 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20170604.12 AB - The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier. VL - 6 IS - 4 ER -