关于S系的覆盖
On covers of S acts

摘要： 设S是幺半群, FGWI, WPF, STF分别表示有限生成弱内射右S系、弱拉回平坦右S系和强挠自由右S系的类。证明了在有左零元的左reversible幺半群上,每一个右S系Ai∈FGWI当且仅当∪[DD(-*3]·[DD)]i∈IAi∈FGWI;在Noetherian幺半群上,任意fg弱内射S系的有向上极限是fg弱内射的;同时考虑了WPF覆盖和STF覆盖,给出了每一个右S系都有FGWI覆盖的条件。证明了若S是有有限几何型的有限生成幺半群,每一个右S系都有WPF覆盖,以及在任意幺半群S上,每一个右S系都有STF覆盖。
Abstract: Let S be a monoid, FGWI, WPF and STF denote the class of finitely generated weakly injective right S acts, weakly pullback flat right S acts and strongly torsion free right Sacts respectively. It is proved that if S is a left reversible monoid with a left zero, then every rightS actAi∈FGWI if and only if the coproduct ∪[DD(-*3]·[DD)]i∈IAi∈FGWI. IfS is a Noetherian monoid, then the directed colimit of fgweakly injective Sacts is fgweakly injective. At the same time, WPF covers and STF covers are investigated, the condition over which every right Sact has a FGWI cover is obtained. It is proved that every right Sact has a WPF cover over a finitely generated monoid with a finite geometric type and every right Sact has a STFcover over any monoid S