Characteristic of Rings. Prime Fields

• Autorzy: Christoph Schwarzweller , Artur Korniłowicz
• Języki publikacji: EN

Abstrakty

EN

The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

Słowa kluczowe

EN

commutative algebra; characteristic of rings; prime field

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 12E05: Polynomials (irreducibility, etc.)
• 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p ; tight closure

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 4
• Strony: 333-349

Daty

wydano

2015-12-01

otrzymano

2015-08-14

online

2016-03-25

Twórcy

autor

Christoph Schwarzweller

• Institute of Computer Science, University of Gdańsk, Poland

autor

Artur Korniłowicz

• Institute of Informatics, University of Białystok, Poland

Bibliografia

• [1] Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565–582, 2001.
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• [14] Nathan Jacobson. Basic Algebra I. 2nd edition. Dover Publications Inc., 2009.
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• [28] Christoph Schwarzweller. The correctness of the generic algorithms of Brown and Henrici concerning addition and multiplication in fraction fields. Formalized Mathematics, 6(3): 381–388, 1997.
• [29] Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29–34, 1999.
• [30] Christoph Schwarzweller. The field of quotients over an integral domain. Formalized Mathematics, 7(1):69–79, 1998.
• [31] Yasunari Shidama, Hikofumi Suzuki, and Noboru Endou. Banach algebra of bounded functionals. Formalized Mathematics, 16(2):115–122, 2008. doi:10.2478/v10037-008-0017-z.[Crossref]
• [32] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.
• [33] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341–347, 2003.
• [34] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990.
• [35] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.
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Identyfikatory

DOI

10.1515/forma-2015-0027

bwmeta1.id-class.MML

RING 3