A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to dis...A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.展开更多
It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ...It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.展开更多
基金The National Natural Science Foundation of China (No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education ( No. 200802860024)+1 种基金the Natural Science Foundation of Jiangsu Province ( No. BK2010393 )Scientific Research Foundation of Guangxi University ( No. XJZ100246)
文摘A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.
基金Supported by the Natural Science Foundation of China (19901009)
文摘It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.
