Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

background: no data is available on morphology and genetic characteristics of echinococcus granulosus derived from donkeys of iran, despite of its existence in donkeys.in the present study morphometric variations of the rostellar hooks of protoscoleces and genotype characteristics of hydatid cyst of donkey from iran were determined. methods: protoscoleces prepared from hydatid cyst of donkey of...