2010, ISBN: 6130349351

[EAN: 9786130349356], Neubuch, [PU: VDM Verlag Dr. Müller E.K.], nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In abstract al… More...

[EAN: 9786130349356], Neubuch, [PU: VDM Verlag Dr. Müller E.K.], nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Englisch, Books<

2010, ISBN: 6130349351

[EAN: 9786130349356], Nieuw boek, [SC: 14.17], [PU: VDM Verlag Dr. Müller E.K.], nach der Bestellung gedruckt Neuware -High Quality Content by WIKIPEDIA articles! In abstract algebra, the… More...

[EAN: 9786130349356], Nieuw boek, [SC: 14.17], [PU: VDM Verlag Dr. Müller E.K.], nach der Bestellung gedruckt Neuware -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. Englisch, Books<

2010, ISBN: 6130349351

[EAN: 9786130349356], Neubuch, [PU: VDM Verlag Dr. Müller E.K. Jan 2010], This item is printed on demand - it takes 3-4 days longer - Neuware -High Quality Content by WIKIPEDIA articles! … More...

[EAN: 9786130349356], Neubuch, [PU: VDM Verlag Dr. Müller E.K. Jan 2010], This item is printed on demand - it takes 3-4 days longer - Neuware -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. Englisch, Books<

2010, ISBN: 6130349351

[EAN: 9786130349356], Neubuch, [PU: Betascript Publishers Jan 2010], Neuware - High Quality Content by WIKIPEDIA articles! In abstract algebra, the term torsion refers to a number of conc… More...

[EAN: 9786130349356], Neubuch, [PU: Betascript Publishers Jan 2010], Neuware - 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. 80 pp. Englisch<

ISBN: 9786130349356

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 module… More...

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, Hörbücher & Kalender / Bücher / Sachbuch / Naturwissenschaften / Mathematik<