In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn...In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.展开更多
For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a...For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.展开更多
For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(x) is the n-th cyclotomic polynomial.At first,by using Faltings' theorem on Mordell conjecture it is proved that if F is a number field an...For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(x) is the n-th cyclotomic polynomial.At first,by using Faltings' theorem on Mordell conjecture it is proved that if F is a number field and if n = 4,8,12 is a positive integer having a square factor then Gn(F) is not a subgroup of K2(F),and then by using the results of Manin,Grauert,Samuel and Li on Mordell conjecture theorem for function fields,a similar result is established for function fields over an algebraically closed field.展开更多
It is proved that neither G9(Q) nor G11(Q) is a subgroup of K2(Q)which confirms two special cases of a conjecture proposed by Browkin, J. (LectureNotes in Math., 966, Springer-Verlag, New York, Heidelberg, Berlin, 198...It is proved that neither G9(Q) nor G11(Q) is a subgroup of K2(Q)which confirms two special cases of a conjecture proposed by Browkin, J. (LectureNotes in Math., 966, Springer-Verlag, New York, Heidelberg, Berlin, 1982, 1-6).展开更多
Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show tha...Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given.展开更多
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K...The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.展开更多
In this paper, we investigate tile structure of K2OF for F = -3 mod 9 and d ≠ -3. We find the element of order 3 of K2OF for F = and generated elements of K2OF /(2) /(8) /(3) for F = . We get the property of 2F, ...In this paper, we investigate tile structure of K2OF for F = -3 mod 9 and d ≠ -3. We find the element of order 3 of K2OF for F = and generated elements of K2OF /(2) /(8) /(3) for F = . We get the property of 2F, which develops a Tate and Bass's theorem, and give the structure of K2OF for F = and the presentation relations of SLn(OF)(n ≥ 3)展开更多
文摘In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.
基金This work wassupported by the National Natural Science Foundation of China (Grant No. 19531020) the National Distinguished Youth Science Foundation of China.
文摘For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.
基金supported by the National Natural Science Foundation of China (Grant No.10371061)
文摘For a field F,let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*},where Φn(x) is the n-th cyclotomic polynomial.At first,by using Faltings' theorem on Mordell conjecture it is proved that if F is a number field and if n = 4,8,12 is a positive integer having a square factor then Gn(F) is not a subgroup of K2(F),and then by using the results of Manin,Grauert,Samuel and Li on Mordell conjecture theorem for function fields,a similar result is established for function fields over an algebraically closed field.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19531020) the National Distinguished Youth Science Foundation of China and China Postdoctoral Science Foundation This work was also partially supported by the Mo
文摘For some local fields F, a description of torsion subgroups of K2 (F) via the elements of a specific form is given.
文摘It is proved that neither G9(Q) nor G11(Q) is a subgroup of K2(Q)which confirms two special cases of a conjecture proposed by Browkin, J. (LectureNotes in Math., 966, Springer-Verlag, New York, Heidelberg, Berlin, 1982, 1-6).
基金Supported by Natural Science Foundation of Anhui Department of Education (Grant No. KJ2008B240)supported by Natural Science Foundation of China (Grant No. 61170172)
文摘Let S be a formal matrix ring, T the subring consisting of all diagonal elements, I the set consisting of all off-diagonal elements. Then I is a split radical ideal under certain conditions. In this paper, we show that K2（S）≈ K2（T） G K2（S, I）, and a presentation of K2（S, I） is given.
文摘The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.
文摘In this paper, we investigate tile structure of K2OF for F = -3 mod 9 and d ≠ -3. We find the element of order 3 of K2OF for F = and generated elements of K2OF /(2) /(8) /(3) for F = . We get the property of 2F, which develops a Tate and Bass's theorem, and give the structure of K2OF for F = and the presentation relations of SLn(OF)(n ≥ 3)
