Editing Ring (mathematics) (section)

== References ==
<!-- Each unclassified reference here should be moved into the appropriate subsection below. -->
{{refbegin}}
* {{cite book
  | last1=Garling |first1= D. J. H.
  | year=2022
  | title=Galois Theory and Its Algebraic Background
  | edition=2nd
  | location=Cambridge
  | publisher = Cambridge University Press
  | isbn= 978-1-108-83892-4
  }}
* {{citation
  | last1=Cohn |first1=Harvey
  | year=1980
  | title=Advanced Number Theory
  | location=New York
  | publisher=Dover Publications
  | isbn=978-0-486-64023-5
  }}
* {{citation
  | last1=Serre |first1=J-P.
  | year=1950
  | title=Applications algébriques de la cohomologie des groupes, I, II, Séminaire Henri Cartan, 1950/51
  | url=http://www.numdam.org/numdam-bin/feuilleter?id=SHC_1950-1951__3_
  }}
* {{citation
  | last1=Serre
  | year=2006
  | title=Lie algebras and Lie groups
  | edition=2nd
  | publisher=Springer
  }} [corrected 5th printing]
{{refend}}

=== General references ===
{{refbegin}}
* {{cite book
  | last=Artin | first=Michael | author-link=Michael Artin
  | year=2018
  | title=Algebra
  | publisher=Pearson
  | edition=2nd
  }}
* {{cite book
  | last1=Atiyah | first1=Michael | author1-link=Michael Atiyah
  | last2=Macdonald | first2=Ian G. | author2-link=Ian G. Macdonald
  | year=1969
  | title=Introduction to commutative algebra
  | publisher=Addison–Wesley
  }}
* {{cite book
  | last1=Bourbaki | first1=N. | author1-link=Nicolas Bourbaki
  | year=1964
  | title=Algèbre commutative
  | publisher=Hermann
  }}
* {{cite book
  | last1=Bourbaki | first1=N. | author1-link=Nicolas Bourbaki
  | year=1989
  | title=Algebra I, Chapters 1–3
  | publisher=Springer
  }}
* {{citation
  | last1=Cohn | first1=Paul Moritz | author1-link=Paul Cohn
  | year=2003
  | title=Basic algebra: groups, rings, and fields
  | publisher=Springer
  | isbn=978-1-85233-587-8
  }}
* {{cite book
  | last=Eisenbud | first=David | author-link=David Eisenbud
  | year=1995
  | title=Commutative algebra with a view toward algebraic geometry
  | publisher=Springer
  | series=Graduate Texts in Mathematics
  | volume=150
  | mr=1322960
  }}
* {{cite book
  | last1=Gallian
  | first1=Joseph A.
  | title=Contemporary Abstract Algebra, Sixth Edition.
  | publisher=Houghton Mifflin
  | year=2006
  | isbn=9780618514717
  }}
* {{cite book
  | last1=Gardner | first1=J.W.
  | last2=Wiegandt | first2=R.
  | year=2003
  | title=Radical Theory of Rings
  | publisher= Chapman & Hall/CRC Pure and Applied Mathematics
  | isbn=0824750330
 }}
* {{cite book
  | last=Herstein | first=I. N. | author-link=Israel Nathan Herstein
  | year=1994
  | others=With an afterword by Lance W. Small
  | title=Noncommutative rings
  | series=Carus Mathematical Monographs
  | volume=15
  | publisher=Mathematical Association of America
  | orig-year=reprint of the 1968 original
  | isbn=0-88385-015-X
  }}
* {{cite book
  | last1=Hungerford | first1=Thomas W.
  | year=1997
  | title=Abstract Algebra: an Introduction, Second Edition.
  | publisher=Brooks/Cole
  | isbn=9780030105593
  }}
* {{cite journal
  | last=Jacobson | first=Nathan | author-link=Nathan Jacobson
  | year=1964
  | title=Structure of rings
  | journal=American Mathematical Society Colloquium Publications
  | volume=37
  | edition=Revised
  }}
* {{cite journal
  | last=Jacobson | first=Nathan | author-link=Nathan Jacobson
  | year=1943
  | title=The Theory of Rings
  | journal=American Mathematical Society Mathematical Surveys
  | volume=I
  }}
* {{cite book
  | last=Jacobson | first=Nathan | author-link=Nathan Jacobson
  | year=2009
  | title=Basic algebra
  | edition=2nd
  | volume=1
  | publisher=Dover
  | isbn=978-0-486-47189-1
  }}
* {{citation
  | last1=Kaplansky | first1=Irving | author1-link=Irving Kaplansky
  | year=1974
  | title=Commutative rings
  | publisher=[[University of Chicago Press]]
  | edition=Revised
  | mr=0345945
  | isbn=0-226-42454-5
  | url=https://archive.org/details/commutativerings00irvi
  }}
* {{cite book
  | last=Lam | first=Tsit Yuen | author-link=Tsit Yuen Lam
  | year=1999
  | title=Lectures on modules and rings
  | series=Graduate Texts in Mathematics
  | volume=189
  | publisher=Springer
  | isbn=0-387-98428-3
  }}
* {{cite book
  | last=Lam | first=Tsit Yuen | author-link=Tsit Yuen Lam
  | year=2001
  | title=A first course in noncommutative rings
  | edition=2nd
  | series=Graduate Texts in Mathematics
  | volume=131
  | publisher=Springer
  | isbn=0-387-95183-0
  }}
* {{cite book
  | last=Lam | first=Tsit Yuen | author-link=Tsit Yuen Lam
  | year=2003
  | title=Exercises in classical ring theory
  | edition=2nd
  | series=Problem Books in Mathematics
  | publisher=Springer
  | isbn=0-387-00500-5
  }}
* {{Lang Algebra|edition=3r}}
* {{citation
  | last1=Lang |first1=Serge
  | year=2005
  | title=Undergraduate algebra
  | edition=3rd
  | publisher=Springer
  | isbn=0-387-22025-9
  }}
* {{cite book
  | last1=Mac Lane |first1=Saunders |author1-link=Saunders Mac Lane
  | last2=Birkhoff |first2=Garrett
  | year=1967
  | title=Algebra
  | publisher=AMS Chelsea
  }}
* {{cite book
  | last1=Matsumura | first1=Hideyuki
  | year=1989
  | title=Commutative Ring Theory
  | publisher=[[Cambridge University Press]]
  | edition=2nd
  | series=Cambridge Studies in Advanced Mathematics
  | isbn=978-0-521-36764-6
  }}
* {{cite web
  | last=Milne | first=J. | date=2012 | id=v2.23
  | title=A primer of commutative algebra
  | url=http://www.jmilne.org/math/xnotes/ca.html
  }}
* {{citation
  | last1=Rotman | first1=Joseph
  | year=1998
  | title=Galois Theory
  | publisher=Springer
  | edition=2nd
  | isbn=0-387-98541-7
  }}
* {{citation
 | last1=van der Waerden
 | first1=Bartel Leendert
 | author1-link=Bartel Leendert van der Waerden
 | title=Moderne Algebra. Teil I
 | publisher=Springer
 | series= Die Grundlehren der mathematischen Wissenschaften
 | volume=33
 | isbn=978-3-540-56799-8
 | year=1930
 | mr=0009016
 | title-link=Moderne Algebra
 }}
* {{cite book
 | last1=Warner
 | first1=Seth
 | title=Modern Algebra
 | publisher=Dover
 | year=1965
 | isbn=9780486663418
}}
* {{cite book
 | first1=Raymond Louis
 | last1=Wilder
 | title=Introduction to Foundations of Mathematics
 | publisher=Wiley
 | year=1965
}}
* {{cite book
 | last1=Zariski
 | first1=Oscar
 | last2=Samuel
 | first2=Pierre
 | title=Commutative Algebra
 | volume=1
 | publisher=Van Nostrand
 | year=1958
}}
{{refend}}

=== Special references ===
{{refbegin}}
* {{citation
 | last1=Balcerzyk
 | first1=Stanisław
 | last2=Józefiak
 | first2=Tadeusz
 | title=Commutative Noetherian and Krull rings
 | location=Chichester
 | publisher=Ellis Horwood Ltd.
 | series=Mathematics and its Applications
 | year=1989
 | isbn=978-0-13-155615-7
}}
* {{citation
 | last1=Balcerzyk
 | first1=Stanisław
 | last2=Józefiak
 | first2=Tadeusz
 | title=Dimension, multiplicity and homological methods
 | location=Chichester
 | publisher=Ellis Horwood Ltd.
 | series=Mathematics and its Applications
 | isbn=978-0-13-155623-2
 | year=1989
}}
* {{cite journal
 | last=Ballieu
 | first=R.
 | title=Anneaux finis; systèmes hypercomplexes de rang trois sur un corps commutatif
 | journal=Ann. Soc. Sci. Bruxelles
 | volume=I
 | issue=61
 | pages=222–227
 | year=1947
}}
* {{cite book
 | last1=Berrick
 | first1=A. J.
 | last2=Keating
 | first2=M. E.
 | title=An Introduction to Rings and Modules with K-Theory in View
 | publisher=Cambridge University Press
 | year=2000
}}
* {{citation
  | last=Cohn | first=Paul Moritz | author1-link=Paul Cohn
  | year=1995
  | title=Skew Fields: Theory of General Division Rings
  | volume=57
  | series=Encyclopedia of Mathematics and its Applications
  | publisher=Cambridge University Press
  | isbn=9780521432177
  | url-access=registration
  | url=https://archive.org/details/skewfieldstheory0000cohn
  }}
* {{cite journal
  | last1=Gilmer | first1=R.
  | last2=Mott | first2=J.
  | year=1973
  | title=Associative Rings of Order
  | journal=Proc. Japan Acad.
  | volume=49
  | pages=795–799
  | doi=10.3792/pja/1195519146
  | doi-access=free
  }}
* {{cite book
 | last1=Harris
 | first1=J. W.
 | last2=Stocker
 | first2=H.
 | title=Handbook of Mathematics and Computational Science
 | publisher=Springer
 | year=1998
}}
* {{cite book
 | last=Isaacs
 | first=I. M.
 | author-link=Martin Isaacs
 | title=Algebra: A Graduate Course
 | publisher=[[American Mathematical Society|AMS]]
 | isbn=978-0-8218-4799-2
 | year=1994
}}
* {{citation
 | last1=Jacobson
 | first1=Nathan
 | author1-link=Nathan Jacobson
 | title=Structure theory of algebraic algebras of bounded degree
 | journal=[[Annals of Mathematics]]
 | issn=0003-486X
 | volume=46
 | issue=4
 | pages=695–707
 | doi=10.2307/1969205
 | jstor=1969205
 | publisher=Annals of Mathematics
 | year=1945
}}
* {{cite book
 | last=Knuth
 | first=D. E.
 | author-link=Donald Knuth
 | title=The Art of Computer Programming
 | volume=2: Seminumerical Algorithms
 | edition=3rd
 | publisher=Addison–Wesley
 | year=1998
}}
* {{cite book
 | last1=Korn
 | first1=G. A.
 | last2=Korn
 | first2=T. M. | author2-link = Theresa M. Korn
 | title=Mathematical Handbook for Scientists and Engineers
 | publisher=Dover
 | year=2000
 | isbn=9780486411477
 | url=https://books.google.com/books?id=xUQc0RZhQnAC&q=ring
}}
* {{cite web |ref={{harvid|Milne|CFT}}
 | last=Milne
 | first=J.
 | title=Class field theory
 | url=http://www.jmilne.org/math/CourseNotes/cft.html
}}
* {{citation
 | last1=Nagata
 | first1=Masayoshi
 | author1-link=Masayoshi Nagata
 | title=Local rings
 | publisher=Interscience Publishers
 | series=Interscience Tracts in Pure and Applied Mathematics
 | year=1962
 | orig-year=1975 reprint
 | mr=0155856
 | volume=13
 | isbn=978-0-88275-228-0
}}
* {{cite book
 | last=Pierce
 | first=Richard S.
 | title=Associative algebras
 | series=Graduate Texts in Mathematics
 | volume=88
 | publisher=Springer
 | year=1982
 | isbn=0-387-90693-2
 | url=https://archive.org/details/associativealgeb00pier_0
}}
* {{citation
 | last=Poonen
 | first=Bjorn
 | author1-link=Bjorn Poonen
 | title=Why all rings should have a 1
 | year=2019
 | journal=Mathematics Magazine
 | volume=92
 | issue=1
 | pages=58−62
 | doi=10.1080/0025570X.2018.1538714
 | url=https://www.jstor.org/stable/48666015
 | jstor=48666015
 | arxiv=1404.0135
 | hdl=1721.1/126525
 }}
* {{citation
 | last=Serre
 | first=Jean-Pierre
 | author1-link=Jean-Pierre Serre
 | title=Local fields
 | series=Graduate Texts in Mathematics
 | volume=67
 | publisher=Springer
 | year=1979
}}
* {{citation
 | last=Springer
 | first=Tonny A.
 | title=Invariant theory
 | series=Lecture Notes in Mathematics
 | volume=585
 | publisher=Springer
 | year=1977
 | url=https://books.google.com/books?id=pTV7CwAAQBAJ&q=ring
 | isbn=9783540373704
}}
* {{citation
 | last=Weibel | first=Charles A.
 | year=2013
 | title=The K-book: An Introduction to Algebraic K-theory
 | url=https://books.google.com/books?id=Ja8xAAAAQBAJ
 | series=Graduate Studies in Mathermatics
 | volume=145
 | publisher=American Mathematical Society
 | isbn=9780821891322
 }} (also [https://sites.math.rutgers.edu/~weibel/Kbook/Kbook.I.pdf online])
* {{cite book
 | last1=Zariski
 | first1=Oscar
 | author1-link=Oscar Zariski
 | last2=Samuel
 | first2=Pierre
 | author2-link=Pierre Samuel
 | title=Commutative algebra
 | series=Graduate Texts in Mathematics
 | volume=28–29
 | publisher=Springer
 | year=1975
 | isbn=0-387-90089-6
}}
{{refend}}

=== Primary sources ===
{{refbegin}}
* {{cite journal
 | last=Fraenkel
 | first=A.
 | author-link=Abraham Fraenkel
 | title=Über die Teiler der Null und die Zerlegung von Ringen
 | journal=J. Reine Angew. Math.
 | volume=1915
 | pages=139–176
 | year=1915
 | issue=145
 | doi=10.1515/crll.1915.145.139
 | s2cid=118962421
 }}
* {{cite journal
 | last=Hilbert
 | first=David
 | author-link=David Hilbert
 | title=Die Theorie der algebraischen Zahlkörper
 | journal=Jahresbericht der Deutschen Mathematiker-Vereinigung
 | volume=4
 | year=1897
}}
* {{cite journal
 | last=Noether
 | first=Emmy
 | author-link=Emmy Noether
 | title=Idealtheorie in Ringbereichen
 | journal=Math. Annalen
 | volume=83
 | issue=1–2
 | pages=24–66
 | year=1921
 | doi=10.1007/bf01464225
 | s2cid=121594471
 | url=https://zenodo.org/record/1428306
 }}
{{refend}}

=== Historical references ===
{{refbegin}}
* Bronshtein, I. N. and Semendyayev, K. A. (2004) [[Bronshtein and Semendyayev|Handbook of Mathematics]], 4th ed. New York: Springer-Verlag {{isbn|3-540-43491-7}}.
* [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Ring_theory.html History of ring theory at the MacTutor Archive]
* {{citation |last1=Birkhoff |first1=Garrett |author1-link=Garrett Birkhoff |last2=Mac Lane| first2=Saunders |author2-link=Saunders Mac Lane |year=1996 |title=A Survey of Modern Algebra |edition=5th |location=New York |publisher=Macmillan }}
* Faith, Carl (1999) ''Rings and things and a fine array of twentieth century associative algebra''. Mathematical Surveys and Monographs, 65. [[American Mathematical Society]] {{isbn|0-8218-0993-8}}.
* Itô, K. editor (1986) "Rings." §368 in ''Encyclopedic Dictionary of Mathematics'', 2nd ed., Vol. 2. Cambridge, MA: [[MIT Press]].
* {{cite journal |last1=Kleiner |first1=Israel |author1-link=Israel Kleiner (mathematician) |year=1996 |title=The Genesis of the Abstract Ring Concept |journal=[[American Mathematical Monthly]] |volume=103 |issue=5 |pages=417–424 |doi=10.2307/2974935 |jstor=2974935 }}
* {{cite journal |last1=Kleiner |first1=Israel |author1-link=Israel Kleiner (mathematician) |title=From Numbers to Rings: The Early History of Ring Theory |journal=[[Elemente der Mathematik]] |date=February 1998 |volume=53 |issue=1 |pages=18–35 |doi=10.1007/s000170050029|doi-access=free }}
* {{citation |last1=van der Waerden |first1=B. L. |year=1985 |author1-link=Bartel Leendert van der Waerden |title=A History of Algebra |publisher=Springer-Verlag }}
{{refend}}

{{Authority control}}

{{DEFAULTSORT:Ring (Mathematics)}}
[[Category:Algebraic structures]]
[[Category:Ring theory]]