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commutative algebra Define commutative algebra Translate commutative algebra commutative algebra in English commutative algebra in French commutative algebra in Italian commutative algebra in Spanish ... Download this dictionary Commutative algebra This page deals with the area of study. For algebras which are commutative, see algebra (disambiguation) .In abstract algebra , commutative algebra studies commutative rings , their ideals , and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings , rings of algebraic integers , including the ordinary integers Z, and p-adic integer s. See more at Wikipedia.org... This article uses material from Wikipedia and is licensed under the GNU Free Documentation License Wikipedia Deutsch Die freie Enzyklop¤die Download this dictionary Kommutative Algebra Eine kommutative Algebra ist eine Algebra , in der das Kommutativgesetz f¼r die Multiplikation erf¼llt ist.Die Kommutative Algebra ist das Teilgebiet der Mathematik im Bereich der Algebra , das sich mit kommutativen Ringen sowie deren Idealen Moduln und Algebren befasst. Sie ist grundlegend f¼r die Gebiete der

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Make eBroadcast my Homepage Contact Us It's Web Guide Encyclopedia Contents Commutative algebra In abstract algebra commutative algebra is the field of study of commutative rings , their ideals modules and algebras . It is foundational both for algebraic geometry and for algebraic number theory Related pages include: integral domain quotient field principal ideal domain unique factorization domain ... Spectrum of a ring The subject's real founder, in the days when it was called ideal theory , should be considered to be David Hilbert . He seems to have thought of it (around 1900) as an alternate approach that could replace the then-fashionable complex function theory . In line with his thinking, computational aspects were secondary to the structural. The additional module concept, present in some form in Kronecker's work, is technically an improvement on working always directly on the special case of ideals . Its adoption is attributed to Emmy Noether 's influence. Given the scheme concept, commutative algebra is reasonably thought of as either the local theory or the affine theory of algebraic geometry Elsewhere Search engine Web directory CONTENTS: A B C D ... Contact Us

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Commutative algebra From Exampleproblems Jump to: navigation search In abstract algebra commutative algebra is the field of study of commutative rings , their ideals modules and algebras . It is foundational both for algebraic geometry and for algebraic number theory . The most prominent example for commutative rings are polynomial rings The subject's real founder, in the days when it was called ideal theory , should be considered to be David Hilbert . He seems to have thought of it (around 1900) as an alternate approach that could replace the then-fashionable complex function theory . In line with his thinking, computational aspects were secondary to the structural. The additional module concept, present in some form in Kronecker 's work, is technically an improvement on working always directly on the special case of ideals . Its adoption is attributed to Emmy Noether 's influence. Given the scheme concept, commutative algebra is reasonably thought of as either the local theory or the affine theory of algebraic geometry The general study of rings that are not required to be commutative is known as noncommutative algebra ; it is pursued in ring theory representation theory and in other areas such as Banach algebra theory.

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Commutative algebra This page deals with the area of study. For algebras which are commutative, see Commutative (ᎦᏁᏟᏴᏍᏗ) ᏗᏎᏍᏗ ᎤᎬᏩᎵ commutative (ᎦᏁᏟᏴᏍᏗ) ᎠᎵᏰᏑᏍᏔᏬ modules (ᎠᎴᏠᏗᏍᎬ) algebraic (ᏗᏎᏍᏗ) ᏗᏎᏍᏗ ᏓᏍᏓᏠᏠalgebraic (ᏗᏎᏍᏗ) ᏎᏍᏗ ᎪᎷᏩᏛᏗ ᎠᏓᏁᎸ ᎠᏁᏍᎬᏗ ᏀᎾ commutative (ᎦᏁᏟᏴᏍᏗ) ᏗᏎᏍᏗ ᎤᎬᏩᎵ. ᏧᏓᏃᏣᎵ examples (ᏱᏓᏟᎶᏍᏔᏠ) commutative (ᎦᏁᏟᏴᏍᏗ) ᏗᎵᏰᏑᏍᏔᏬ ᎠᏠᏯᏍᏛ polynomial ᎠᎵᏰᏑᏍᏔᏬ algebraic (ᏗᏎᏍᏗ) integers (ᏂᎦᏛ) integer (ᏂᎦᏛ) Z p-adic integer (ᏂᎦᏛ) Commutative (ᎦᏁᏟᏴᏍᏗ) ᏗᏎᏍᏗ ᎤᎬᏩᎵ ᎨᏒᎢ ᎯᎠ ᏄᎬᏫᏳᏒ ᎤᏦᏍᏗ ᏂᎬᎿᏠᎪᎱᏍᏗ ᎬᏔᏂᏓᏍᏗ ᎭᏫᎾᏗᏢ ᎯᎠ ᎾᎥᎢ ᎠᎦᏎᏍᏙᏗ schemes (ᎠᏓᏠᏖᏗ) ᎯᎠ ᎠᎦᏎᏍᏙᏗ ᏗᎵᏰᏑᏍᏔᏬ ᎦᏙ ᎤᏍᏗ ᎾᏍᎩ ᏂᎨᏒᎾ ᎠᏎᎾᏍᎩ ᎢᏳᎵᏍᏙᏗ commutative (ᎦᏁᏟᏴᏍᏗ) ᎨᏒᎢ ᏓᎪᏍᎬ noncommutative (ᎥᏝ ᎦᏁᏟᏴᏍᏗ) ᏗᏎᏍᏗ ᎤᎬᏩᎵ Banach ᏗᏎᏍᏗ ᎤᎬᏩᎵ External (ᎤᏓᏎᎦᏤᏗ) ᏗᏕᎬᏔᏛ Richard (ᎤᏪᎾᎢ ᎠᏍᏓᏯ) Dedekind (ᎥᏝ ᏧᎬᏩᎶᏗ ᎠᎦᏘᏯ ᎤᏓᏠᏗ) ... David Hilbert generalize (ᏂᎦᎥ) ᎯᎠ ᎢᎬᏱᎨᏍᏙᏗ ᎠᎴᏂᏍᎬ . Hilbert ᎬᏂᎨᏒ ᏄᏩᏁᎸ ᎤᏟ ᎢᎦᎢ ᎠᏓᏓᎶᏙᏗ ᎤᎾᏄᎪᎢᏍᏗ ᏠᎪᏢᎯᏐᏗ ᎯᎠ ᎤᏟ ᎢᎦᎢ ᎠᏰᏍᏛᏗ ᎠᎴ computationally (ᏗᏎᏍᏗ) oriented (ᎣᏂᏯᎨᏍᏙᏗ) ᎢᏗᎬᎾᏗ grounded (ᎦᏙᎯ) ᎭᏫᎾᏗᏢ ᏯᏛᎿ ᏧᏓᎴᏠᏓ ᏥᏄᏍᏗ

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D ynamic Content Item one Item two Item three Item four ... Home search a topic Item one Item two Item three Item four ... Item five This page deals with the area of study. For algebras which are commutative, see algebra (disambiguation) Commutative algebra is the branch of abstract algebra that studies commutative rings , their ideals , and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings , rings of algebraic integers , including the ordinary integers Z , and p-adic integers Commutative algebra is the main technical tool in the local study of schemes The study of rings which are not necessarily commutative is known as noncommutative algebra ; it includes ring theory representation theory , and the theory of Banach algebras Contents History See also References External links [edit History The subject, first known as ideal theory , began with Richard Dedekind 's work on ideals , itself based on the earlier work of Ernst Kummer and Leopold Kronecker . Later

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