This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP...This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP） ring; （2） If R is an α-rigid ring, then R is a Baer （PP, PS） ring if and only if R[x, x^-1; α] is a Baer （PP, PS） ring.展开更多
By constructing a Gray map, a class of constacyclic codes over ring R = R＋ vR is studied. Using cyclic codes and negacyclic codes of length p^s over ring R, the structure of （1 - 2v）-constacyclic codes and dual cod...By constructing a Gray map, a class of constacyclic codes over ring R = R＋ vR is studied. Using cyclic codes and negacyclic codes of length p^s over ring R, the structure of （1 - 2v）-constacyclic codes and dual codes of length p^s over ring R are given, the Gray images of （1 - 2v）-constacyclic codes in a particular case are also studied. It is shown that linear codes of length pS over ring R are （1 -2v）-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p^s over ring R.展开更多
基金the Program for New Century Excellent Talents in University(04-0522),and the National Natural Science Foundation of China(10571153)
文摘This paper gives some results on Strong-Armendariz rings and the Ore-extensions R[x,x^-1;α] of Bare, PP and PS rings. And the main two results are： （1） R is a Bear （PP） ring if and only if R[[x]] is a Baer （PP） ring; （2） If R is an α-rigid ring, then R is a Baer （PP, PS） ring if and only if R[x, x^-1; α] is a Baer （PP, PS） ring.
基金supported by the National Natural Science Foundation of China under Grant No.61370089
文摘By constructing a Gray map, a class of constacyclic codes over ring R = R＋ vR is studied. Using cyclic codes and negacyclic codes of length p^s over ring R, the structure of （1 - 2v）-constacyclic codes and dual codes of length p^s over ring R are given, the Gray images of （1 - 2v）-constacyclic codes in a particular case are also studied. It is shown that linear codes of length pS over ring R are （1 -2v）-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p^s over ring R.
