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References

  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  2. [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  3. [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  5. [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  8. [8] Jing-Chao Chen. The Steinitz theorem and the dimension of a real linear space. FormalizedMathematics, 6(3):411-415, 1997.
  9. [9] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  10. [10] Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Z-modules. Formalized Mathematics, 20(1):47-59, 2012, doi: 10.2478/v10037-012-0007-z.10.2478/v10037-012-0007-z
  11. [11] Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of Z-module. Formalized Mathematics, 20(3):205-214, 2012, doi: 10.2478/v10037-012-0024-y.10.2478/v10037-012-0024-y
  12. [12] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.
  13. [13] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  14. [14] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.
  15. [15] Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.10.1007/978-1-4615-0897-7_8
  16. [16] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.
  17. [17] Michał Muzalewski and Wojciech Skaba. From loops to abelian multiplicative groups with zero. Formalized Mathematics, 1(5):833-840, 1990.
  18. [18] Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.
  19. [19] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  20. [20] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  21. [21] Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.
  22. [22] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
  23. [23] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  24. [24] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990.
  25. [25] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  26. [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  27. [27] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  28. [28] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
DOI: https://doi.org/10.2478/v10037-012-0033-x | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 275 - 280
Published on: Feb 2, 2013
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2013 Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.