本文旨在推广钱国华老师的特征标余次数。设G1和G2是两个有限群,χξ,χζ分别是G1和G2的任意不可约特征标,复合得到的特征标χξ#ζ是G1×G2的不可约特征标。我们探讨了G1×G2的特征标余次数cod(χξ#ζ)与G1的特征标余次数cod...本文旨在推广钱国华老师的特征标余次数。设G1和G2是两个有限群,χξ,χζ分别是G1和G2的任意不可约特征标,复合得到的特征标χξ#ζ是G1×G2的不可约特征标。我们探讨了G1×G2的特征标余次数cod(χξ#ζ)与G1的特征标余次数cod(χξ)及G2的特征标余次数cod(χζ)之间的数量关系,并在此基础上对原有特征标余次数的相关性质进行了推广和拓展。This paper aims to extend the definition of character codegrees as presented by Professor Qian Guohua. Let G1and G2be two finite groups, with χξand χζbeing arbitrary irreducible characters of G1and G2, respectively. The combined character χξ#ζis an irreducible character of G1×G2. We explore the quantitative relationship between the character codegree cod(χξ#ζ)ofG1×G2, the character codegrees cod(χξ)of G1, and cod(χζ)of G2. Based on this relationship, we extend and expand the properties of the original character codegrees.展开更多
Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两...Du Xianneng和Chen Zhengxin用Gorenstein内射模刻画了Gorenstein环.作者根据Gorenstein投射模来刻画Gorenstein环,利用推出图,得到了定理3.由该文可以看出n-Gorenstein环与Gorenstein投射模的对应关系.在此基础上,又得到了定理4中的两个结论的等价性,在一定意义上拓展了Gorenstein投射模的有关结论.展开更多
文摘本文旨在推广钱国华老师的特征标余次数。设G1和G2是两个有限群,χξ,χζ分别是G1和G2的任意不可约特征标,复合得到的特征标χξ#ζ是G1×G2的不可约特征标。我们探讨了G1×G2的特征标余次数cod(χξ#ζ)与G1的特征标余次数cod(χξ)及G2的特征标余次数cod(χζ)之间的数量关系,并在此基础上对原有特征标余次数的相关性质进行了推广和拓展。This paper aims to extend the definition of character codegrees as presented by Professor Qian Guohua. Let G1and G2be two finite groups, with χξand χζbeing arbitrary irreducible characters of G1and G2, respectively. The combined character χξ#ζis an irreducible character of G1×G2. We explore the quantitative relationship between the character codegree cod(χξ#ζ)ofG1×G2, the character codegrees cod(χξ)of G1, and cod(χζ)of G2. Based on this relationship, we extend and expand the properties of the original character codegrees.
