The complete integral closure of monoids and domains II

Using geometrical methods we construct primary monoids whose complete integral closure is not completely integrally closed. Such monoids cannot be realized as multiplicative monoids of integral domains with finitely generated groups of divisibility. Complete integral closure, Primary monoids

On the generalized Davenport constant and the Noether number

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page

Some closure operations in Zariski-Riemann spaces of valuation domains: a survey

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains

Investigations into a putative role for the novel BRASSIKIN pseudokinases in compatible pollen-stigma interactions in Arabidopsis thaliana.

BACKGROUND: In the Brassicaceae, the early stages of compatible pollen-stigma interactions are tightly controlled with early checkpoints regulating pollen adhesion, hydration and germination, and pollen tube entry into the stigmatic surface. However, the early signalling events in the stigma which trigger these compatible interactions remain unknown. RESULTS: A set of stigma-expressed pseudokinase genes, termed BRASSIKINs (BKNs), were identified and found to be present in only core Brassicaceae genomes. In Arabidopsis thaliana Col-0, BKN1 displayed stigma-specific expression while the BKN2 gene was expressed in other tissues as well. CRISPR deletion mutations were generated for the two tandemly linked BKNs, and very mild hydration defects were observed for wild-type Col-0 pollen when placed on the bkn1/2 mutant stigmas. In further analyses, the predominant transcript for the stigma-specific BKN1 was found to have a premature stop codon in the Col-0 ecotype, but a survey of the 1001 Arabidopsis genomes uncovered three ecotypes that encoded a full-length BKN1 protein. Furthermore, phylogenetic analyses identified intact BKN1 orthologues in the closely related outcrossing Arabidopsis species, A. lyrata and A. halleri. Finally, the BKN pseudokinases were found to be plasma-membrane localized through the dual lipid modification of myristoylation and palmitoylation, and this localization would be consistent with a role in signaling complexes. CONCLUSION: In this study, we have characterized the novel Brassicaceae-specific family of BKN pseudokinase genes, and examined the function of BKN1 and BKN2 in the context of pollen-stigma interactions in A. thaliana Col-0. Additionally, premature stop codons were identified in the predicted stigma specific BKN1 gene in a number of the 1001 A. thaliana ecotype genomes, and this was in contrast to the out-crossing Arabidopsis species which carried intact copies of BKN1. Thus, understanding the function of BKN1 in other Brassicaceae species will be a key direction for future studies

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

narrating traditional iranian carpet merchants

Iranian carpet merchants developed a collective identitary narrative to enhance their capital creation in the social field of the German market, the field of Iranian foreign trade, and transnational bazari networks. This chapter goes beyond the practicalities of juggling resources across social fields: it explains the motivation behind this agency. Building on David Graeber's anthropology of value, as well as on studies about identity marketing and ethnic entrepreneurship, I show how the merchants' resources were evaluated between the 1950s and today to explain by which systems of value these social fields were shaped. From the confrontation between changing systems of value emerges Iranian carpet merchants' potential to increase the efficiency of their capital creation by—collectively—trying to redefine the meaning of their resources