This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether ce...This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.展开更多
We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p > 3congruent to...We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p > 3congruent to 3 modulo 4, the component e(p+1)/2of the p-Sylow subgroup of the ideal class group of Q(ζp) is trivial.展开更多
The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a fu...The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a function δ is called a generalized derivation. Suppose that U is a Lie ideal of R such that u^2 ∈ U for all u ∈ U. In this paper, we prove that U lahtain in Z（R） when one of the following holds： （1） δ（[u, v]） = u o v =（2） δ（[u,v]）=[u o v] = 0 （3） δ（u o v） = [u, v] （4） δ（u o v）＋δ[u, v] = 0 for all u, v ∈ U.展开更多
基金supported by a National Key Basic Research Project of ChinaNSFC
文摘This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension field.Using this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.
基金Supported by National Natural Science Foundation of China(Grant No.11171141)Natural Science Foundation of Jiangsu Province of China(Grant Nos.BK2010007)the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(Grant No.708044)
文摘We compute the density of primes represented by a special quadratic form in a fixed square residue class. Using this result and a new method introduced by Thaine we prove the fact that for a prime p > 3congruent to 3 modulo 4, the component e(p+1)/2of the p-Sylow subgroup of the ideal class group of Q(ζp) is trivial.
文摘The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a function δ is called a generalized derivation. Suppose that U is a Lie ideal of R such that u^2 ∈ U for all u ∈ U. In this paper, we prove that U lahtain in Z（R） when one of the following holds： （1） δ（[u, v]） = u o v =（2） δ（[u,v]）=[u o v] = 0 （3） δ（u o v） = [u, v] （4） δ（u o v）＋δ[u, v] = 0 for all u, v ∈ U.
