Normal Sections and Direct Product Decompositions

Abstract

In any finitely complete category, there is an internal notion of normal monomorphism. We give elementary conditions guaranteeing that a normal section s: Y → X of an arrow f: X → Y produces a direct product decomposition of the form X ? Y × W. We then show how these conditions gradually vanish in various algebraic contexts, such as Maltsev, protomodular and additive categories.     

Dimension inequalities for the closure of the image of a multilinear function

In this note we give a simple proof and an extension of a dimension inequality of Howard concerning the range of a multilinear function with vector space range by using some results on algebraic varieties.     

Bundles over the Fano Threefold V 5

ABSTRACT

Using an explicit resolution of the diagonal for the variety V ₅, we provide cohomological characterizations of the universal and quotient bundles. A splitting criterion for bundles over V ₅ is also proved.

The presentation of semistable aCM bundles is shown, together with a resolution–theoretic classification of low rank aCM bundles.     

Complete Congruences on the Lattice of Rees–Sushkevich Varieties

We study the lattice ?(RS_n) of subvarieties of the variety of semigroups generated by completely 0-simple semigroups over groups with exponent dividing n, with a particular focus on the lattice ??(RS_n) consisting of those varieties that are generated by completely 0-simple semigroups. The sublattice of ??(RS_n) consisting of the aperiodic varieties is described and several endomorphisms of ?(RS_n) considered. The complete congruence on ??(RS_n) that relates varieties containing the same aperiodic completely 0-simple semigroups is considered in some detail.     

Bioactive constituents of Iris hybrida (Iridaceae): Processing effect

Iris genus plants are a valuable source of bioactive compounds, which are an important component for pharmaceutical development. The present article shows the potential for mineral nutrition with application of magnesium sulfate, iron chelates and potassium oxide affecting the phenolic compound contents in Iris hybrida ‘Tsikavynka’, I. hybrida ‘Tambo’ and I. hybridа ‘Widecombe Fire’. The effect of mineral processing was specific to plant organs and varied in the component composition. The Iris rhizomes had an increased total phenolic compound content after treatment (up to 10% of the total isoflavonoid content, up to 8% of phenolic acids, up to 5% of γ-pyrones and up to 13% of flavonoids), determined using UV–vis spectroscopy. A positive effect of nutrition on the biosynthesis and content of individual isoflavonoids (tectoridin, nigricin d -glucoside, genistin, iristectorigenin B, nigricin, irigenin and irisolidone) and xanthone mangiferin in Iris rhizomes by HPLC was established. In addition, an increase in the chlorogenic acid amount in Iris leaves was noted. The results demonstrate the sensitivity of Iris phenylpropanoid metabolism to mineral nutrition and can be used to predict medical plant cultivation with increased content of bioactive constituents.