»ã±¨±êÌâ (Title)£ºAuslander-type Conditions and Weakly Gorenstein Algebras£¨AuslanderÐÍÇ°ÌáºÍÈõGorenstein´úÊý£©

»ã±¨ÈË (Speaker)£º»ÆÕ×Ó¾½ÌÊÚ£¨ÄϾ©´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê6ÔÂ9ÈÕ(ÖÜÎå) 15:00-15:50

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£º¸ßéª

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»ã±¨ÌáÒª£ºLet R be an Artin algebra. Auslander and Reiten conjectured that R is Gorenstein if R satisfies the Auslander condition. We prove that if R is left quasi Auslander, then R is Gorenstein if and only if it is (left and) right weakly Gorenstein, and that if R satisfies the Auslander condition, then R is Gorenstein if and only if it is left or right weakly Gorenstein. This is a reduction of the above conjecture.