The main objects of the present paper are (i) Hibi rings (toric arising from order polytopes posets), (ii) stable set perfect graphs), and (iii) edge graphs satisfying odd cycle condition). goal is to analyze those three toric discuss their structures in case where class groups have small rank. We prove that (i), torsionfree. More precisely, we give descriptions groups. Moreover, characterize p...

Elastic stability of ring and stringer-stiffened cylindrical shells under axial, internal and external pressures is studied using Ritz method. The stiffeners are rings, stringers and their different arrangements at the inner and outer surfaces of the shell. Critical buckling loads are obtained using Ritz method. It has been found that the cylindrical shells with outside rings are more stable th...

One o f the ma in aims o f [5] is to obta in bounds for asr(A) for var ious classes of noncommuta t i ve rings A; in part icular , they show that: (i) asr(A) ~< 1 + d whenever A is a module finite a lgebra over a commuta t ive Noe ther ian ring R with d im(maxspec R) = d, and (ii) asr(A) = 1 if A is a semi-local ring (see [5], Theorems 3.1 and 2.4], respectively). The a im o f this note is to s...

That is, a ring of rank n is a ring (commutative, associative, with unit) whose underlying additive group is isomorphic to Z. The prototypical examples of rings of rank n are, of course, orders in degree n number fields. The class of all such examples consists precisely of those rings of rank n that are integral domains. However, there are many interesting examples of rings of rank n that are n...