Have a personal or library account? Click to login
Groups – Additive Notation Cover
By: Roland Coghetto  
Open Access
|Aug 2015

References

  1. [1] Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565-582, 2001.
  2. [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  3. [3] Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.
  4. [4] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.
  5. [5] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  6. [6] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  7. [7] Grzegorz Bancerek. Zermelo theorem and axiom of choice. Formalized Mathematics, 1 (2):265-267, 1990.
  8. [8] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
  9. [9] Richard E. Blahut. Cryptography and Secure Communication. Cambridge University Press, 2014.10.1017/CBO9781139013673
  10. [10] Sylvie Boldo, Catherine Lelay, and Guillaume Melquiond. Formalization of real analysis: A survey of proof assistants and libraries. Mathematical Structures in Computer Science, pages 1-38, 2014.
  11. [11] Nicolas Bourbaki. General Topology: Chapters 1-4. Springer Science and Business Media, 2013.
  12. [12] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  13. [13] Czesław Bylinski. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643-649, 1990.
  14. [14] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  15. [15] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  16. [16] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  17. [17] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  18. [18] Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
  19. [19] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  20. [20] Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.
  21. [21] 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
  22. [22] Edwin Hewitt and Kenneth A. Ross. Abstract Harmonic Analysis: Volume I. Structure of Topological Groups. Integration. Theory Group Representations, volume 115. Springer Science and Business Media, 2012.
  23. [23] Johannes Hölzl, Fabian Immler, and Brian Huffman. Type classes and filters for mathematical analysis in Isabelle/HOL. In Interactive Theorem Proving, pages 279-294. Springer, 2013.10.1007/978-3-642-39634-2_21
  24. [24] Teturo Inui, Yukito Tanabe, and Yositaka Onodera. Group theory and its applications in physics, volume 78. Springer Science and Business Media, 2012.
  25. [25] Artur Korniłowicz. The definition and basic properties of topological groups. Formalized Mathematics, 7(2):217-225, 1998.
  26. [26] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829-832, 1990.
  27. [27] Christopher Norman. Basic theory of additive Abelian groups. In Finitely Generated Abelian Groups and Similarity of Matrices over a Field, Springer Undergraduate Mathematics Series, pages 47-96. Springer, 2012. ISBN 978-1-4471-2729-1. doi:10.1007/978-1-4471-2730-7 2.10.1007/978-1-4471-2730-7
  28. [28] Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991.
  29. [29] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  30. [30] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  31. [31] Alexander Yu. Shibakov and Andrzej Trybulec. The Cantor set. Formalized Mathematics, 5(2):233-236, 1996.
  32. [32] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4): 535-545, 1991.
  33. [33] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115-122, 1990.
  34. [34] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
  35. [35] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
  36. [36] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
  37. [37] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1 (2):369-376, 1990.
  38. [38] Andrzej Trybulec. Baire spaces, Sober spaces. Formalized Mathematics, 6(2):289-294, 1997.
  39. [39] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.
  40. [40] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  41. [41] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  42. [42] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990.
  43. [43] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.
  44. [44] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  45. [45] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  46. [46] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  47. [47] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  48. [48] Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.
DOI: https://doi.org/10.1515/forma-2015-0013 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 127 - 160
Submitted on: Apr 30, 2015
|
Published on: Aug 13, 2015
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:

© 2015 Roland Coghetto, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.