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Torsion (Algebra) - Lambert M. Surhone#Miriam T. Timpledon#Susan F. Marseken
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Lambert M. Surhone#Miriam T. Timpledon#Susan F. Marseken:

Torsion (Algebra) - neues Buch

2010, ISBN: 9786130349356

ID: 532983376

High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Let G be a group. An element g of G is called a torsion element if g has finite order. If all elements of G are torsion, then G is called a torsion group. If the only torsion element is the identity element, then the group G is called torsion-free. Let M be a module over a ring R without zero divisors. An element m of M is called a torsion element if the cyclic submodule of M generated by m is not free. Equivalently, m is torsion if and only if it has a non-zero annihilator in R. If the ring R is commutative, then the set of all torsion elements forms a submodule of M, called the torsion submodule of M, sometimes denoted T(M). The module M is called a torsion module if T(M) = M, and is called torsion-free if T(M) = 0. If the ring R is non-commutative then the situation is more complicated, and the set of torsion elements need not be a submodule. Nevertheless, it is a submodule given the assumption that the ring R satisfies the Ore condition. This covers the case when R is a Noetherian domain. Abstract Algebra, Group (Mathematics), Periodic Group, Identity Element, Free Abelian Group, Pure Subgroup, Finitely Generated Module, Analytic Torsion Bücher > Fremdsprachige Bücher > Englische Bücher Taschenbuch 01.01.2010, Betascript Publishing, .201

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Torsion (Algebra) - Lambert M. Surhone#Miriam T. Timpledon#Susan F. Marseken
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Lambert M. Surhone#Miriam T. Timpledon#Susan F. Marseken:

Torsion (Algebra) - neues Buch

ISBN: 9786130349356

ID: 6936488500d708c21763673ab6ebe1b2

Abstract Algebra, Group (Mathematics), Periodic Group, Identity Element, Free Abelian Group, Pure Subgroup, Finitely Generated Module, Analytic Torsion High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Let G be a group. An element g of G is called a torsion element if g has finite order. If all elements of G are torsion, then G is called a torsion group. If the only torsion element is the identity element, then the group G is called torsion-free. Let M be a module over a ring R without zero divisors. An element m of M is called a torsion element if the cyclic submodule of M generated by m is not free. Equivalently, m is torsion if and only if it has a non-zero annihilator in R. If the ring R is commutative, then the set of all torsion elements forms a submodule of M, called the torsion submodule of M, sometimes denoted T(M). The module M is called a torsion module if T(M) = M, and is called torsion-free if T(M) = 0. If the ring R is non-commutative then the situation is more complicated, and the set of torsion elements need not be a submodule. Nevertheless, it is a submodule given the assumption that the ring R satisfies the Ore condition. This covers the case when R is a Noetherian domain. Bücher / Fremdsprachige Bücher / Englische Bücher 978-613-0-34935-6, Betascript Publishing

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Torsion (Algebra) - Taschenbuch

ISBN: 6130349351

Gebundene Ausgabe, ID: 6082278

Abstract Algebra, Group (Mathematics), Periodic Group, Identity Element, Free Abelian Group, Pure Subgroup, Finitely Generated Module, Analytic Torsion - Buch, gebundene Ausgabe, 80 S., Beilagen: Paperback, Erschienen: 2010 Betascript Publishers High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Let G be a group. An element g of G is called a torsion element if g has finite order. If all elements of G are torsion, then G is called a torsion group. If the only torsion element is the identity element, then the group G is called torsion-free. Let M be a module over a ring R without zero divisors. An element m of M is called a torsion element if the cyclic submodule of M generated by m is not free. Equivalently, m is torsion if and only if it has a non-zero annihilator in R. If the ring R is commutative, then the set of all torsion elements forms a submodule of M, called the torsion submodule of M, sometimes denoted T(M). The module M is called a torsion module if T(M) = M, and is called torsion-free if T(M) = 0. If the ring R is non-commutative then the situation is more complicated, and the set of torsion elements need not be a submodule. Nevertheless, it is a submodule given the assumption that the ring R satisfies the Ore condition. This covers the case when R is a Noetherian domain.

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Torsion (Algebra) - neues Buch

ISBN: 9786130349356

ID: e0ee1fd11b7d8788db069e8b281d93ff

High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Let G be a group. An element g of G is called a torsion element if g has finite order. If all elements of G are torsion, then G is called a torsion group. If the only torsion element is the identity element, then the group G is called torsion-free. Let M be a module over a ring R without zero divisors. An element m of M is called a torsion element if the cyclic submodule of M generated by m is not free. Equivalently, m is torsion if and only if it has a non-zero annihilator in R. If the ring R is commutative, then the set of all torsion elements forms a submodule of M, called the torsion submodule of M, sometimes denoted T(M). The module M is called a torsion module if T(M) = M, and is called torsion-free if T(M) = 0. If the ring R is non-commutative then the situation is more complicated, and the set of torsion elements need not be a submodule. Nevertheless, it is a submodule given the assumption that the ring R satisfies the Ore condition. This covers the case when R is a Noetherian domain. Buch / Broschur

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Torsion (Algebra) - Taschenbuch

2010, ISBN: 6130349351

Gebundene Ausgabe, ID: 6082278

Abstract Algebra, Group (Mathematics), Periodic Group, Identity Element, Free Abelian Group, Pure Subgroup, Finitely Generated Module, Analytic Torsion - Buch, gebundene Ausgabe, 80 S., Beilagen: Paperback, Erschienen: 2010 Betascript Publishers

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Torsion (Algebra)
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Titel:

Torsion (Algebra)

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6130349351

High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Let G be a group. An element g of G is called a torsion element if g has finite order. If all elements of G are torsion, then G is called a torsion group. If the only torsion element is the identity element, then the group G is called torsion-free. Let M be a module over a ring R without zero divisors. An element m of M is called a torsion element if the cyclic submodule of M generated by m is not free. Equivalently, m is torsion if and only if it has a non-zero annihilator in R. If the ring R is commutative, then the set of all torsion elements forms a submodule of M, called the torsion submodule of M, sometimes denoted T(M). The module M is called a torsion module if T(M) = M, and is called torsion-free if T(M) = 0. If the ring R is non-commutative then the situation is more complicated, and the set of torsion elements need not be a submodule. Nevertheless, it is a submodule given the assumption that the ring R satisfies the Ore condition. This covers the case when R is a Noetherian domain.

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EAN (ISBN-13): 9786130349356
ISBN (ISBN-10): 6130349351
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2010
Herausgeber: Betascript Publishing

Buch in der Datenbank seit 01.01.2009 15:16:35
Buch zuletzt gefunden am 20.10.2016 15:47:57
ISBN/EAN: 6130349351

ISBN - alternative Schreibweisen:
613-0-34935-1, 978-613-0-34935-6

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