As a particular one parameter deformation of the quantum determinant, we introduce a quantum αdeterminant det (α) q and study the Uq(gln)-cyclic module generated by it: We show that the multiplicity of each irreducible representation in this cyclic module is determined by a certain polynomial called the q-content discriminant. A part of the present result is a quantum counterpart for the result...

we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

The notion of a tensor product of topological groups and modules is important in theory of topological groups, algebraic number theory. The tensor product of compact zero-dimensional modules over a pseudocompact algebra was introduced in [B] and for the commutative case in [GD], [L]. The notion of a tensor product of abelian groups was introduced in [H]. The tensor product of modules over commu...

The so called dense pairings were studied mainly by D. Radford in his work on coreflexive coalegbras over fileds [Rad73]. They were generalized in [G-T98] and [AG-TL2001] to the so called rational pairings over commutative ground rings to study the interplay between the comodules of an R-coalgebra C and the modules of an R-algebra A that admits an R-algebra morphism κ : A −→ C∗. Such pairings, ...

Fidelity of chromosome segregation relies on coordination of chromosome biorientation and the spindle checkpoint. Central to this is the kinetochore scaffold KNL1 that integrates the functions of various mitotic regulators including BUB1 and BUBR1. We show that KNL1 contains an extensive array of short linear sequence modules that encompass TxxΩ and MELT motifs and that can independently locali...

The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...