We study the structure of cyclic codes of length 2k?over Z8?for any natural number k.? It is known that cyclic codes of length 2k?over Z8?are ideals of the ring R=Z8[X]/. In this paper we prove that the ring R=Z8[X]/ ...We study the structure of cyclic codes of length 2k?over Z8?for any natural number k.? It is known that cyclic codes of length 2k?over Z8?are ideals of the ring R=Z8[X]/. In this paper we prove that the ring R=Z8[X]/ is a local ring with unique maximal ideal, thereby implying that R is not a principal ideal ring.? We also prove that cyclic codes of length?2k?over Z8?are generated as ideals by at most three elements.展开更多
This paper deals with a reducible sl(2,C)action on the formal power series ring.The purpose of this paper is to confirm a special case of the Yau conjecture:Suppose that sl(2,C)acts on the formal power series ring via...This paper deals with a reducible sl(2,C)action on the formal power series ring.The purpose of this paper is to confirm a special case of the Yau conjecture:Suppose that sl(2,C)acts on the formal power series ring via(1.1).Then I(f)=(li 1 )⊕(il2 )⊕···⊕(lis)modulo some one dimensional sl(2,C)representations where(i)is an irreducible sl(2,C)representation of i dimension and{li1 ,li2 ,...,lis }{ll1,ll2,...,lr}.Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations,we treat the reducible action and higher dimensional representations successively.展开更多
By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring o...By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring of rr x n polynomial matrices is a principal ideal and principal one-sided ideal ring.展开更多
文摘We study the structure of cyclic codes of length 2k?over Z8?for any natural number k.? It is known that cyclic codes of length 2k?over Z8?are ideals of the ring R=Z8[X]/. In this paper we prove that the ring R=Z8[X]/ is a local ring with unique maximal ideal, thereby implying that R is not a principal ideal ring.? We also prove that cyclic codes of length?2k?over Z8?are generated as ideals by at most three elements.
基金supported by National Natural Science Foundation of China(Grant No.10731030) and PSSCS of Shanghai
文摘This paper deals with a reducible sl(2,C)action on the formal power series ring.The purpose of this paper is to confirm a special case of the Yau conjecture:Suppose that sl(2,C)acts on the formal power series ring via(1.1).Then I(f)=(li 1 )⊕(il2 )⊕···⊕(lis)modulo some one dimensional sl(2,C)representations where(i)is an irreducible sl(2,C)representation of i dimension and{li1 ,li2 ,...,lis }{ll1,ll2,...,lr}.Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations,we treat the reducible action and higher dimensional representations successively.
文摘By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring of rr x n polynomial matrices is a principal ideal and principal one-sided ideal ring.
