Some observations on left absolutely flat monoids

Communicated by J.M. Howie     

Flatness Properties of Acts: Some Examples

Research supported by Natural Sciences and Engineering Research Council of Canada Grant A4494 Research supported by Estonian Science Foundation Grant 930     

Flatness Properties of S-Posets

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomology group vanishes.     

Tensor products and preservation of limits, for acts over monoids

In 1971, Stenström published one of the first papers devoted to the problem of when, for a monoid S and a right S -act A _S , the functor A? (from the category of left acts over S into the category of sets) has certain limit preservation properties. Attention at first focused on when this functor preserves pullbacks and equalizers but, since that time, a large number of related articles have appeared, most having to do with when this functor preserves monomorphisms of various kinds. All of these properties are often referred to as flatness properties of acts . Surprisingly, little attention has so far been paid to the obvious questions of when A _S ? preserves all limits, all finite limits, all products, or all finite products. The present article addresses these matters.     

On left absolutely flat monoids

Communicated by J. M. Howie