Conservation Rules of Direct Sum Decomposition of Groups
References
- [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- [2] Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990.
- [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [4] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.
- [5] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.
- [6] Nicolas Bourbaki. Elements of Mathematics. Algebra I. Chapters 1-3. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989.
- [7] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
- [8] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [10] Artur Korniłowicz. The product of the families of the groups. Formalized Mathematics, 7(1):127-134, 1998.
- [11] Serge Lang. Algebra. Springer, 3rd edition, 2005.
- [12] Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, and Yasunari Shidama. Definition and properties of direct sum decomposition of groups. Formalized Mathematics, 23 (1):15-27, 2015. doi:10.2478/forma-2015-0002.
- [13] D. Robinson. A Course in the Theory of Groups. Springer New York, 2012.
- [14] J.J. Rotman. An Introduction to the Theory of Groups. Springer, 1995.
- [15] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
- [16] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5): 855-864, 1990.
- [17] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573-578, 1991.
- [18] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
Language: English
Page range: 81 - 94
Submitted on: Dec 31, 2015
Published on: Aug 31, 2016
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Keywords:
Related subjects:
© 2016 Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.