n-absorbing ideal factorization of commutative rings

In this article, we show that Mori domains, pseudo-valuation domains, and $n$-absorbing ideals, the three seemingly unrelated notions in commutative ring theory, are interconnected. In particular, we prove that an integral domain $R$ is a Mori locally pseudo-valuation domain if and only if each proper ideal of $R$ is a finite product of 2-absorbing ideals of $R$. Moreover, every ideal of a Mori locally almost pseudo-valuation domain can be written as a finite product of 3-absorbing ideals. To provide concrete examples of such rings, we study rings of the form $A+XB[X]$ where $A$ is a subring of a commutative ring $B$ and $X$ is indeterminate, which is of independent interest, and along with several characterization theorems, we prove that in such a ring, each proper ideal is a finite product of $n$-absorbing ideals for some $n\ge 2$ if and only if $A$ and $B$ are both Artinian reduced rings and the contraction map $\text{Spec}(B)\to\text{Spec}(A)$ is a bijection. A complete description of when an order of a quadratic number field is a locally pseudo valuation domain, a locally almost pseudo valuation domain or a locally conducive domain is given

On SS-nn-absorbing ideals

Let $R$ be a commutative ring with identity, $S$ a multiplicative subset of $R$ and $I$ an ideal of $R$ disjoint from $S$. In this paper, we introduce the notion of an $S$-$n$-absorbing ideal which is a generalization of both the $S$-prime ideals and $n$-absorbing ideals. Moreover, we investigate the basic properties, quotient extension, existence and amalgamation of $S$-$n$-absorbing ideals.Comment: 18page

Stability of hydrogenation states of graphene and conditions for hydrogen spillover

The hydrogen spillover mechanism has been discussed in the field of hydrogen storage and is believed to have particular advantage over the storage as metal or chemical hydrides. We investigate conditions for practicality realizing the hydrogen spillover mechanism onto carbon surfaces, using first-principles methods. Our results show that contrary to common belief, types of hydrogenation configurations of graphene (the aggregated all-paired configurations) can satisfy the thermodynamic requirement for room-temperature hydrogen storage. However, the peculiarity of the paired adsorption modes gives rise to a large kinetic barrier against hydrogen migration and desorption. It means that an extremely high pressure is required to induce the migration-derived hydrogenation. However, if mobile catalytic particles are present inside the graphitic interstitials, hydrogen migration channels can open and the spillover phenomena can be realized. We suggest a molecular model for such a mobile catalyst which can exchange hydrogen atoms with the wall of graphene.open151