Given a commutative ring R (respectively a positively graded commutative ring A = ⊕j>0Aj which is finitely generated as an A0-algebra), a bijection between the torsion classes of finite type in ModR (respectively tensor torsion classes of finite type in QGrA) and the set of all subsets Y ⊆ Spec R (respectively Y ⊆ Proj A) of the form Y = S i∈Ω Yi, with Spec R \ Yi (respectively Proj A \ Yi) qua...

In this paper, some familiar and new results on arithmetical rings, modules, Bezout rings (not necessarily commutative) are provided. particular, we examine relationships between their localizations by maximal ideals, saturated submodules saturations, localizable properties of annihilators finitely generated modules over diagonalizable with flat right quasi-projective Hermite Pierce stalks, Kru...

The properties of matrix valued polynomials generated by the scalartype Rodrigues’ formulas are analyzed. A general representation of these polynomials is found in terms of products of simple differential operators. The recurrence relations, leading coefficients, completeness are established, as well as, in the commutative case, the second order equations for which these polynomials are eigenfu...

Let M be an infinite unitary module over a commutative ring R with identity. Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. These modules have been studied by several algebraists, including Robert Gilmer, Bill Heinzer, and the author. In this note, we recall the major results on Jónsson modules to bring the reader up to speed on current re...

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the co...

Let R be a finite commutative ring. We prove that a MacWilliams type relation between the m-spotty weight enumerators of a linear code over R and its dual hold, if and only if, R is a Frobenius (equivalently, Quasi-Frobenius) ring, if and only if, the number of maximal ideals and minimal ideals of R are the same, if and only if, for every linear code C over R, the dual of the dual C is C itself...

Let a be an ideal of commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a-finiteness and a-cohomological dimensions are equal. In particular, we examine relative analogues quasi-Buchsbaum, Buchsbaum surjective modules. reveal several interactions between these types modules that extend some the existing results in classical theory to one.

The algebra of Free Quasi-Symmetric Functions FQSym [5] is a graded algebra of noncommutative polynomials whose bases are parametrized by permutations. Under commutative image, it is mapped onto Gessel’s algebra of quasi-symmetric functions, whence its name. Quasi-symmetric functions generalize symmetric functions in a natural way, and many classical results admit quasi-symmetric extensions or ...

We present a candidate supergravity solution for a stacked configuration of stable non-BPS D-branes in Type II string theory compactified on T /Z2. This gives a supergravity description of nonabelian tachyon condensation on the brane worldvolume. BROWN-HET-1263 IC/2001/27