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  1. Repozytorium Uniwersytetu w Białymstoku
  2. Czasopisma naukowe / Journals
  3. Formalized Mathematics
  4. Formalized Mathematics, 2015, Volume 23, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/4907
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    Pole DCWartośćJęzyk
    dc.contributor.authorSchwarzweller, Christophpl
    dc.contributor.authorKorniłowicz, Arturpl
    dc.date.accessioned2016-12-16T10:30:41Z-
    dc.date.available2016-12-16T10:30:41Z-
    dc.date.issued2015pl
    dc.identifier.citationFormalized Mathematics, Volume 23, Issue 4, 333–349pl
    dc.identifier.issn1426-2630pl
    dc.identifier.issn1898-9934pl
    dc.identifier.urihttp://hdl.handle.net/11320/4907-
    dc.description.abstractThe 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.pl
    dc.language.isoenpl
    dc.publisherDe Gruyter Openpl
    dc.subjectcommutative algebrapl
    dc.subjectcharacteristic of ringspl
    dc.subjectprime fieldpl
    dc.titleCharacteristic of Rings. Prime Fieldspl
    dc.typeArticlepl
    dc.identifier.doi10.1515/forma-2015-0027pl
    dc.description.AffiliationChristoph Schwarzweller - Institute of Computer Science, University of Gdańsk, Polandpl
    dc.description.AffiliationArtur Korniłowicz - Institute of Informatics, University of Białystok, Polandpl
    dc.description.referencesJonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565–582, 2001.pl
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.pl
    dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.pl
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.pl
    dc.description.referencesJózef Białas. Group and field definitions. Formalized Mathematics, 1(3):433–439, 1990.pl
    dc.description.referencesCzesław Byliński. Binary operations. Formalized Mathematics, 1(1):175–180, 1990.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.pl
    dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.pl
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.pl
    dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.pl
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.pl
    dc.description.referencesYuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Set of points on elliptic curve in projective coordinates. Formalized Mathematics, 19(3):131–138, 2011. doi:10.2478/v10037-011-0021-6. [Crossref]pl
    dc.description.referencesYuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, and Yasunari Shidama. Gaussian integers. Formalized Mathematics, 21(2):115–125, 2013. doi:10.2478/forma-2013-0013. [Crossref]pl
    dc.description.referencesNathan Jacobson. Basic Algebra I. 2nd edition. Dover Publications Inc., 2009.pl
    dc.description.referencesAndrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841–845, 1990.pl
    dc.description.referencesArtur Korniłowicz and Christoph Schwarzweller. The first isomorphism theorem and other properties of rings. Formalized Mathematics, 22(4):291–301, 2014. doi:10.2478/forma-2014-0029. [Crossref]pl
    dc.description.referencesJarosław Kotowicz. Quotient vector spaces and functionals. Formalized Mathematics, 11 (1):59–68, 2003.pl
    dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990.pl
    dc.description.referencesRafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829–832, 1990.pl
    dc.description.referencesHeinz Lüneburg. Die grundlegenden Strukturen der Algebra (in German). Oldenbourg Wisenschaftsverlag, 1999.pl
    dc.description.referencesAnna Justyna Milewska. The field of complex numbers. Formalized Mathematics, 9(2): 265–269, 2001.pl
    dc.description.referencesMichał Muzalewski. Opposite rings, modules and their morphisms. Formalized Mathematics, 3(1):57–65, 1992.pl
    dc.description.referencesMichał Muzalewski. Category of rings. Formalized Mathematics, 2(5):643–648, 1991.pl
    dc.description.referencesMichał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3–11, 1991.pl
    dc.description.referencesMichał Muzalewski and Wojciech Skaba. From loops to Abelian multiplicative groups with zero. Formalized Mathematics, 1(5):833–840, 1990.pl
    dc.description.referencesKarol Pąk. Linear map of matrices. Formalized Mathematics, 16(3):269–275, 2008. doi:10.2478/v10037-008-0032-0. [Crossref]pl
    dc.description.referencesChristoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559–564, 2001.pl
    dc.description.referencesChristoph 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.pl
    dc.description.referencesChristoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29–34, 1999.pl
    dc.description.referencesChristoph Schwarzweller. The field of quotients over an integral domain. Formalized Mathematics, 7(1):69–79, 1998.pl
    dc.description.referencesYasunari 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]pl
    dc.description.referencesAndrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.pl
    dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341–347, 2003.pl
    dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990.pl
    dc.description.referencesWojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573–578, 1991.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.pl
    dc.description.referencesB.L. van der Waerden. Algebra I. 4th edition. Springer, 2003.pl
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.pl
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    Formalized Mathematics, 2015, Volume 23, Issue 4

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