Embedding Principle for Rings and Abelian Groups-Reference-Cited by-同舟云学术

Embedding Principle for Rings and Abelian Groups

Published:2023-09-01 Issue:1 Volume:31 Page:143-150
ISSN:1898-9934
Container-title:Formalized Mathematics
language:en
Short-container-title:

Author:

Watase Yasushige¹

Affiliation:

1. 1 Suginami-ku Matsunoki 6 , Tokyo , Japan

Abstract

Summary The article concerns about formalizing a certain lemma on embedding of algebraic structures in the Mizar system, claiming that if a ring A is embedded in a ring B then there exists a ring C which is isomorphic to B and includes A as a subring. This construction applies to algebraic structures such as Abelian groups and rings.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics

Link

https://www.sciendo.com/pdf/10.2478/forma-2023-0013

Reference12 articles.

1. Michael Francis Atiyah and Ian Grant Macdonald. Introduction to Commutative Algebra, volume 2. Addison-Wesley Reading, 1969.

2. 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.

3. Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.

4. Edward J. Barbeau. Polynomials. Springer, 2003.

5. Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.