caa a22 4500 605519099 CHVBK 20210128100728.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10559-015-9758-1 doi (NATIONALLICENCE)springer-10.1007/s10559-015-9758-1 Invariance of Keys with Respect to Operations of Table Algebras [Elektronische Daten] [V. Red'ko, D. Buy, A. Senchenko] The problem of invariance of keys including simple keys is investigated as applied to operations of table algebras that are modern analogues of classical relational Codd algebras. It is shown that the keys being considered are invariant with respect to the operations of intersection, difference, selection, join, and division, but invariance does not hold for simple keys. The keys including simple keys are shown to be invariant with respect to the renaming operation. Necessary and sufficient conditions under which such keys including simple keys are invariant with respect to the operations of projection and active supplement are established. The results of this work are of theoretical and practical interest and can be used to choose optimal keys in designing relational databases. Springer Science+Business Media New York, 2015 database nationallicence table algebra nationallicence key nationallicence Red'ko V. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut Buy D. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut Senchenko A. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/5(2015-09-01), 667-675 1060-0396 51:5<667 2015 51 10559 https://doi.org/10.1007/s10559-015-9758-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10559-015-9758-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Red'ko V. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Buy D. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Senchenko A. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut NATIONALLICENCE 773 0- Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/5(2015-09-01), 667-675 1060-0396 51:5<667 2015 51 10559