Perinormalitas di Daerah Krull (Perinormality on Krull Domains)

Daerah integral R dikatakan perinormal jika untuk setiap overring (lokal) T dari R yang memenuhi kondisi going-down, maka T merupakan lokalisasi dari R pada ideal prima. Perinormalitas merupakan salah satu sifat ketertutupan integral. Dengan memperhatikan bahwa klosur integral dari daerah normal Noether merupakan daerah Krull, akan ditunjukkan bagaimana sifat perinormalitas di daerah Krull.An integral domain R is said to be perinormal if whenever T is a (local) overring of R such that the inclusion R in T satisfies going-down, it follows that T is a localization of R necessarily at a prime ideal. Perinormality is one of integral closedness property. As the integral closure of any Noetherian normal domain is Krull, it will be shown how perinormality behaves on Krull domains.

Hes genes regulate sequential stages of neurogenesis in the olfactory epithelium

We have characterised the functions of the bHLH transcriptional repressors HES1 and HES5 in neurogenesis, using the development of the olfactory placodes in mouse embryos as a model. Hes1 and Hes5 are expressed with distinct patterns in the olfactory placodes and are subject to different regulatory mechanisms. Hes1 is expressed in a broad placodal domain, which is maintained in absence of the neural determination gene Mash1. In contrast, expression of Hes5 is restricted to clusters of neural progenitor cells and requires Mash1 function. Mutations in Hes1 and Hes5 also have distinct consequences on olfactory placode neurogenesis. Loss of Hes1 function leads both to expression of Mash1 outside of the normal domain of neurogenesis and to increased density of MASH1-positive progenitors within this domain, and results in an excess of neurons after a delay. A mutation in Hes5 does not produce any apparent defect. However, olfactory placodes that are double mutant for Hes1 and Hes5 upregulate Ngn1, a neural bHLH gene activated downstream of Mash1, and show a strong and rapid increase in neuronal density. Together, our results suggest that Hes1 regulates Mash1 transcription in the olfactory placode in two different contexts, initially as a prepattern gene defining the placodal domain undergoing neurogenesis and, subsequently, as a neurogenic gene controlling the density of neural progenitors in this domain. Hes5 synergizes with Hes1 and regulates neurogenesis at the level of Ngn1 expression. Therefore, the olfactory sensory neuron lineage is regulated at several steps by negative signals acting through different Hes genes and targeting the expression of different proneural gene homologs.