Strong Morita equivalence of semigroups with local units

In this paper we study Morita contexts for semigroups. We prove a Rees matrix cover connection between strongly Morita equivalent semigroups and investigate how the existence of a unitary Morita semigroup over a given semigroup is related to the existence of a ‘good’ Rees matrix cover of this semigroup.     

Wreath Product of Set-Valued Functors and Tensor Multiplication

Considering the wreath product functor $G wr H:{\cal A} wr^G{\cal B} \rightarrow \SET$ of functors $G: {\cal A}\rightarrow \SET$ and $H: {\cal B}\rightarrow \SET$ over small categories $ {\cal A}$ and $ {\cal B}$, we prove that if tensor multiplication by the functor $G\wrr H$ preserves $ {\cal D}$-limits, where ${\cal D}$ is a small category, then tensor multiplication by $G$ preserves ${\cal D}$-limits, and if tensor multiplication by the functor $G wr H$ preserves ${\cal D}$-limits of representables then tensor multiplications by $G$ and $H$ preserve $ {\cal D}$-limits of representables. We also study flatness and pullback flatness of the wreath product of set-valued functors.     

When Torsion Free Acts are Principally Weakly Flat

A necessary and sufficient condition for principal weak flatness of all right torsion free acts over a monoid is found. It is shown that the corresponding class of monoids is a proper subclass of left PP monoids.     

Morita invariants for semigroups with local units

In this paper we study Morita invariants for strongly Morita equivalent semigroups with local units of various kinds. Among others we prove that, under a certain condition of this kind, congruence lattices are preserved by strong Morita equivalence.     

Morita equivalence of finite semigroups

Semigroup Forum - Two semigroups are called Morita equivalent if the categories of firm right acts over them are equivalent. We prove that every semigroup is Morita equivalent to its subsemigroup...     

Self-assembling of Mn12 molecular nanomagnets on FIB-patterned Au dot matrix

We have developed a novel strategy to build arrays of magnetic nanodots on the 100 nm scale, which exploits the potentialities of both bottom-up and top-down approaches, by self-assembling sulfur-functionalized Mn12 single molecule magnets (SMMs) on patterned Au dot matrices nanofabricated by FIB (focus ion beam). In this way, we demonstrate the capability to assemble SMMs in ordered arrays, where the magnetic information can be easily addressed, being the single bit represented by a 2D distribution of few hundred Mn12 clusters, grafted on top of each 100 × 100 nm² Au dot. Moreover, the chosen Mn12 functionalization is expected to favour a preferential orientation of the grafted molecule with the easy magnetization axis normal to the surface.     

On Descent Theory for Monoid Actions

We give some sufficient conditions for a monoid homomorphism to be an effective descent morphism.     

Isolated Mn12 single-molecule magnets grafted on gold surfaces via electrostatic interactions

Electrostatic interactions drive the adsorption of polycationic single-molecule magnets onto anionic monolayers self-assembled on gold surfaces. Well-isolated magnetic clusters have been deposited and characterized using scanning tunneling microscopy and X-ray photoemission spectroscopy.