Let K be a perfect field and let k ⊂ K be a subfield. In [4, Theorem 3.2], left finite dimensional simple two-sided k-central vector spaces over K were classified by arithmetic data associated to the extension K/k. In this paper, we continue to study the relationship between simple two-sided vector spaces and their associated arithmetic data. In particular, we determine which arithmetic data co...

In this paper, we consider meromorphic extension of the function \[ \zeta_{h^{\left( r\right) }}\left( s\right) =\sum_{k=1}^{\infty} \frac{h_{k}^{\left( }}{k^{s}},\text{ }\operatorname{Re}\left( >r, \] (which call \textit{hyperharmonic zeta function}) where $h_{n}^{(r)}$ are hyperharmonic numbers. We establish certain constants, denoted $\gamma_{h^{\left( m\right) $, which naturally occur in La...

Let Λ be a left and right noetherian ring and mod Λ the category of finitely generated left Λ-modules. In this paper we show the following statements: (1) For a positive integer k the condition that the subcategory of mod Λ consisting of i-torsionfree modules coincides with the subcategory of mod Λ consisting of i-syzygy modules for any 1 ≤ i ≤ k is left-right symmetric. (2) If Λ is an Auslande...

It is well known that the distance metric plays an important role in the clustering process. Indeed, many clustering problems can be treated as an optimization problem of a criterion function defined over one distance metric. While many distance metrics have been developed, it is not clear that how these distance metrics can impact on the clustering/optimization process. To that end, in this pa...

The effects of possible right-handed weak hadronic currents in rare exclusive semileptonic decays B → (K, K *)ν ¯ ν are investigated using a lattice-constrained dispersion quark model for the calculation of the relevant mesonic form factors. The results obtained for the branching ratios and the missing energy spectra are presented and the sensitivity of various observables to long-distance phys...

Let $R$ be a ring and $M$ be a right $R$-module. In this paper, we give some properties of self-cogeneratormodules. If $M$ is self-cogenerator and $S = End_{R}(M)$ is a cononsingular ring, then $M$ is a$mathcal{K}$-module. It is shown that every self-cogenerator Baer is dual Baer.

Let be a left and right noetherian ring and mod the category of finitely generated left -modules. In this article, we show the following results. 1 For a positive integer k, the condition that the subcategory of mod consisting of i-torsionfree modules coincides with the subcategory of mod consisting of i-syzygy modules for any 1 ≤ i ≤ k is left-right symmetric. 2 If is an -Gorenstein ring and N...