the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post’s Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such i...

Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend ...

Computational methods for finding the character table of a finite group require a stock of reducible characters and techniques for decomposing these characters into irreducible characters. A method for generating reducible characters from a representation of a group is proposed. Several new techniques for computing the irreducible decompositions of a set of characters are given; these technique...

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

Abstract Given a continuous, odd, reducible, and semi-simple $2$-dimensional representation $\bar \rho _{0}$ of $G_{{\mathbb{Q}},Np}$ over finite field odd characteristic $p$, we study the relation between universal deformation ring pseudo-representation corresponding to (pseudo-deformation ring) big $p$-adic Hecke algebra prove that maximal reduced quotient pseudo-deformation is isomorphic loc...

In this paper we determine all non-trivial self-motions of TSSM manipulators with two parallel rotary axes which equals the determination of all flexible octahedra where one vertex is an ideal point. This study also closes the classification of these motions for the whole set of parallel manipulators of TSSM type. Our approach is based on Kokotsakis meshes and the reducible compositions of sphe...

We describe a new 1 + 1 dimensional N = (2, 2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints. It has the advantages that its prepotentials shift by semi chiral superfields under gauge transformations. We also see that the multiplet r...