All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogenous ideals of R(M) have the form I (+)N , where I is an ideal of R and N a submodule of M such that IM ⊆ N . A ring R (M) is called a homogeneous ring if every ideal of R (M) is homogeneous. In this paper we continue our recent work on the idealization of m...

For a nonnegative weakly irreducible tensor, its spectral radius is an eigenvalue corresponding to unique positive eigenvector up scalar, called Perron vector. But including the vector, it may have more than one radius. The projective eigenvariety associated with set of eigenvectors considered in complex space. We prove that dimension above zero, i.e. there are finitely many scalar. characteriz...

Abstract We transfer several elementary geometric properties of rigid-analytic spaces to the world adic spaces, more precisely category which are locally (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular, irreducible components), and Stein factorization theorem. Most notably, we show that morphism in our is automatically open if target nor...

2 Regimes of 1D gases 2 2.1 Strongly versus weakly interacting regimes . . . . . . . . . . . . . . . . . . . . 4 2.2 Nearly ideal gas regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Quasi-condensate regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 Phase fluc...

In this paper, some characterizations of median and quasi-median graphs are extended to general isometric subgraphs of Cartesian products using the concept of an imprint function as introduced by Tardif. This extends the well-known concepts of medians in median graphs as well as imprints in quasi-median graphs. We introduce absolute C-median graphs in analogy to absolute retracts, and derive a ...

Consider an ideal I ⊂ R = C[x 1 ,. .. , x n ] defining a complex affine variety X ⊂ C n. We describe the components associated to I by means of numerical primary decomposition (NPD). The method is based on the construction of deflation ideal I (d) that defines the deflated variety X (d) in a complex space of higher dimension. For every embedded component there exists d and an isolated component...

This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We st...

A max-plus matrixA is called weakly stable if the sequence (orbit) x,A⊗x, A2⊗x, . . . does not reach an eigenvector of A for any x unless x is an eigenvector. This is in contrast to previously studied strongly stable (robust) matrices for which the orbit reaches an eigenvector with any nontrivial starting vector. Max-plus matrices are used to describe multiprocessor interactive systems for whic...

The irreducible representations of the double cover of SL(m) with infinitesmal character 1p having a maximal primitive ideal are determined. We investigate whether these representations are attached to a nilpotent orbit and use the orbit method to speculate their K types. We conclude with a character formula expressing the representations as a sum of simpler virtual representions. Thesis Superv...