Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules L(M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which L(M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz’ “weakly compressible” modules. In particular w...

The activation of carbon monoxide by oxygen on Mg(100) surface has been investigated by X-ray photoelectron spectroscopy (XPS). Carbon monoxide is only weakly adsorbed (dispersion-type forces) on a magnesium surface. The XPS result has shown that the dissociation of carbon monoxide leading to the formation of a metastable surface carbonate species occurs through the participation of an oxyg...

the activation of carbon monoxide by oxygen on mg(100) surface has been investigated by x-ray photoelectron spectroscopy (xps). carbon monoxide is only weakly adsorbed (dispersion-type forces) on a magnesium surface. the xps result has shown that the dissociation of carbon monoxide leading to the formation of a metastable surface carbonate species occurs through the participation of an oxygen s...

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...