Gelanggang (matematika): Perbedaan antara revisi
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Baris 95:
:* gelanggang tanpa identitas perkalian: ''rng'' atau ''pseudo-ring'',<ref>Bourbaki, p. 98.</ref> tapi yang kedua bisa jadi membingungkan karena punya arti lain.
==
{{Wikibooks|Aljabar Abstrak/Gelanggang}}
{{Div col|colwidth=18em}}
* [[Aljabar di atas cincin komutatif]]
* [[Kategori gelanggang]]
* [[Glosarium teori gelanggang]]
* [[Gelanggang non-asosiatif]]
* [[Himpunan gelanggang]]
* [[Semigelanggang]]
* [[Spektrum gelanggang]]
* [[Gelanggang komutatif sederhana]]
{{Div col end}}
Jenis gelanggang khusus:
{{Div col|colwidth=22em}}
* [[Gelanggang Boolean]]
* [[Gelanggang Dedekind]]
* [[Gelang diferensial]]
* [[Bidang eksponensial | Gelanggang eksponensial]]
* [[Gelanggang terbatas]]
* [[Gelanggang Lie]]
* [[Gelanggang lokal]]
* [[Gelanggang Noetherian | Noetherian]] dan [[Gelanggang Artinian]]
* [[Gelanggang urutan]]
* [[Gelanggang Poisson]]
* [[Gelanggang pengurangan]]
* [[Gelanggang reguler]]
* [[Gelanggang periode]]
* [[Gelanggang SBI]]
* [[Nilai gelanggang]] dan [[gelanggang nilai diskrit]]
{{Div col end}}
== Kutipan ==
{{reflist|30em}}
== Referensi ==
=== Referensi umum ===
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* {{Cite book
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}}
{{refend}}
=== Referensi khusus ===
{{refbegin}}
* {{Citation
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| last2=Józefiak
| first2=Tadeusz
| title=Commutative Noetherian and Krull rings
| publisher=Ellis Horwood Ltd.
| location=Chichester
| series=Mathematics and its Applications
| year=1989
| isbn=978-0-13-155615-7
}}
* {{Citation
| last1=Balcerzyk
| first1=Stanisław
| last2=Józefiak
| first2=Tadeusz
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* {{Cite journal
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| title=Anneaux finis; systèmes hypercomplexes de rang trois sur un corps commutatif
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}}
* {{Cite book
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| title=An Introduction to Rings and Modules with K-Theory in View
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* {{Citation
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| title=Skew Fields: Theory of General Division Rings
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* {{Citation
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* {{Cite journal
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| title=Associative Rings of Order
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* {{Cite book
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* {{Citation
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| author1-link=Nathan Jacobson
| title=Structure theory of algebraic algebras of bounded degree
| journal=[[Annals of Mathematics]]
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* {{Cite book
| last1=Korn
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| first2=T. M.
| title=Mathematical Handbook for Scientists and Engineers
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| year=2000
| isbn=9780486411477
| url=https://books.google.com/books?id=xUQc0RZhQnAC&q=ring
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* {{Cite web
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| first=J.
| title=Class field theory
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* {{Citation
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| first1=Masayoshi
| author1-link=Masayoshi Nagata
| title=Local rings
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| series=Interscience Tracts in Pure and Applied Mathematics
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| orig-year=1975 reprint
| mr=0155856
| volume=13
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| title=Associative algebras
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* {{Citation
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| title=Why all rings should have a 1
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}}
* {{Citation
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| title=Local fields
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* {{Citation
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| title=Invariant theory
| series=Lecture Notes in Mathematics
| volume=585
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| url=https://books.google.com/books?id=pTV7CwAAQBAJ&q=ring
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{{refend}}
=== Sumber primer ===
{{refbegin}}
* {{Cite journal
| last=Fraenkel
| first=A.
| author-link=Abraham Fraenkel
| title=Über die Teiler der Null und die Zerlegung von Ringen
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| volume=145
| pages=139–176
| year=1915
}}
* {{Cite journal
| last=Hilbert
| first=David
| author-link=David Hilbert
| title=Die Theorie der algebraischen Zahlkörper
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}}
* {{Cite journal
| last=Noether
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| 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}}
=== Referensi sejarah ===
{{refbegin}}
* [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Ring_theory.html History of ring theory at the MacTutor Archive]
* [[Garrett Birkhoff]] and [[Saunders Mac Lane]] (1996) ''A Survey of Modern Algebra'', 5th ed. New York: Macmillan.
* 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}}.
* 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]].
* [[Israel Kleiner (mathematician)|Israel Kleiner]] (1996) "The Genesis of the Abstract Ring Concept", [[American Mathematical Monthly]] 103: 417–424 {{doi|10.2307/2974935}}
* Kleiner, I. (1998) "From numbers to rings: the early history of ring theory", [[Elemente der Mathematik]] 53: 18–35.
* [[B. L. van der Waerden]] (1985) ''A History of Algebra'', Springer-Verlag,
{{refend}}
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