Let F = Q( √ d) be a real quadratic field with ring of integers O. In this paper we analyze the number hd of GL1(O)orbits of homothety classes of perfect unary forms over F as a function of d. We compute hd exactly for square-free d ≤ 200000. By relating perfect forms to continued fractions, we give bounds on hd and address some questions raised by Watanabe, Yano, and Hayashi.

Let X be any partially ordered set, R any commutative ring, and T = I * (X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z) = {x ∈ X : x z for some z ∈ Z}, and M = Te Z. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.

In this paper, we investigate the existence problem of perfect linear codes over the ring Z4 of integers modulo 4 with respect to homogenous metric. Mathematics Subject Classification: 94B05; 94B60

Perfect codes and minimal distance of a code have great importance in the study of theory of codes. The perfect codes are classified generally and in particular for the Lee metric. However, there are very few perfect codes in the Lee metric. The Lee metric has nice properties because of its definition over the ring of integers residue modulo q. It is conjectured that there are no perfect codes ...

Let k be a perfect field of characteristic p > 0. Using Dieudonné modules, we describe the exact conditions under which a Witt subgroup, i.e., a finite subgroup scheme of Wn, lifts to the ring of Witt Vectors W (k).

Here we explore in silico an alternative to make planar eight π-electron bare ring systems with substitutions of some cyclooctatetraene ring carbon atoms by heavier group 14 elements. We found that the most stable eight membered rings with formulae C(4)Si(4)H(8), C(4)Ge(4)H(8), and C(4)Sn(4)H(8) have a perfect planar structure, enhancing delocalization energy as compared to cot.

The transparency of contacts between conjugated molecules and metallic single-walled carbon nanotubes is investigated using a single-particle Green's function method which combines a Landauer approach with ab initio density functional theory. We find that the overall conjugation required for good contact transparency is broken by connecting through a six-member ring on the tube. Full conjugatio...

We previously showed that the inverse limit of standard-graded polynomial rings with perfect (or semiperfect) coefficient field is a ring in an uncountable number variables. In this paper, we show result holds no hypothesis on field. also prove analogous for ultraproducts rings.

We investigate the perfect derived category dgPer(A) of a positively graded differential graded (dg) algebra A whose degree zero part is a dg subalgebra and semisimple as a ring. We introduce an equivalent subcategory of dgPer(A) whose objects are easy to describe, define a t-structure on dgPer(A) and study its heart. We show that dgPer(A) is a Krull-RemakSchmidt category and consider the case ...