When is a regular local ring a locality?

When is the ring of real measurable functions a hereditary ring?

‎Let $M(X‎, ‎mathcal{A}‎, ‎mu)$ be the ring of real-valued measurable functions‎ ‎on a measure space $(X‎, ‎mathcal{A}‎, ‎mu)$‎. ‎In this paper‎, ‎we characterize the maximal ideals in the rings of real measurable functions‎ ‎and as a consequence‎, ‎we determine when $M(X‎, ‎mathcal{A}‎, ‎mu)$ is a hereditary ring.

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

rigid resolution of a finitely generated module over a regular local ring

Chromophores in Molecular Nanorings: When Is a Ring a Ring?

The topology of a conjugated molecule plays a significant role in controlling both the electronic properties and the conformational manifold that the molecule may explore. Fully π-conjugated molecular nanorings are of particular interest, as their lowest electronic transition may be strongly suppressed as a result of symmetry constraints. In contrast, the simple Kasha model predicts an enhancem...

Every Local Ring Is Dominated by a One-dimensional Local Ring

Let (R; m) be a local (Noetherian) ring. The main result of this paper asserts the existence of a local extension ring S of R such that (i) S dominates R, (ii) the residue eld of S is a nite purely transcendental extension of R=m, (iii) dim(S) 1. In addition, it is shown that S can be obtained so that either mS is the maximal ideal of S or S is a localization of a nitely generated R-algebra.