东南大学学报（英文版）
東南大學學報（英文版）
동남대학학보（영문판）
JOURNAL OF SOUTHEAST UNIVERSITY
2011年
3期
347-350
,共4页
自正交模%自内射性%对偶模%倾斜对
自正交模%自內射性%對偶模%傾斜對
자정교모%자내사성%대우모%경사대
selforthogonal module%selfinjective%dual module%tilting pair
在一个Artin代数Λ上,如果模C和T都是自正交模且满足条件T∈ad(d) C和C∈ad(d)T,则模对(C,T)称为倾斜对.讨论了倾斜对的对偶性,探讨在何种条件下一个倾斜对的对偶仍然是一个倾斜对.给出了一个Artin代数上的模对(D(T),D(C))成为一个n-倾斜对的充分必要条件.同时也给出了一个自内射Artin代数上的模对(T*,C*)成为一个n-倾斜对的充分必要条件.
在一箇Artin代數Λ上,如果模C和T都是自正交模且滿足條件T∈ad(d) C和C∈ad(d)T,則模對(C,T)稱為傾斜對.討論瞭傾斜對的對偶性,探討在何種條件下一箇傾斜對的對偶仍然是一箇傾斜對.給齣瞭一箇Artin代數上的模對(D(T),D(C))成為一箇n-傾斜對的充分必要條件.同時也給齣瞭一箇自內射Artin代數上的模對(T*,C*)成為一箇n-傾斜對的充分必要條件.
재일개Artin대수Λ상,여과모C화T도시자정교모차만족조건T∈ad(d) C화C∈ad(d)T,칙모대(C,T)칭위경사대.토론료경사대적대우성,탐토재하충조건하일개경사대적대우잉연시일개경사대.급출료일개Artin대수상적모대(D(T),D(C))성위일개n-경사대적충분필요조건.동시야급출료일개자내사Artin대수상적모대(T*,C*)성위일개n-경사대적충분필요조건.
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 ∈ ad(d) C and C ∈ ad(d) 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(T),D(C) ) being an n-tilting pair over an Artin algebra for an n-tilting pair ( C,T) 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,T) is also given.
