Invertibility of ideals in prüfer extensions

Using the general approach to invertibility for ideals in ring extensions given by Knebush and Zhang in [9], we investigate about connections between faithfully atness and invertibility for ideals in rings with zero divisors

Genetic parameters for milk somatic cell score and relationships with production traits in primiparous dairy sheep

A total of 13,066 first-lactation test-day records of 2,277 Valle del Belice ewes from 17 flocks were used to estimate genetic parameters for somatic cell scores (SCS) and milk production traits, using a repeatability test-day animal model. Heritability estimates were low and ranged from 0.09 to 0.14 for milk, fat, and protein yields, and contents. For SCS, the heritability of 0.14 was relatively high. The repeatabilities were moderate and ranged from 0.29 to 0.47 for milk production traits. The repeatability for SCS was 0.36. Flock-test-day explained a large proportion of the variation for milk production traits, but it did not have a big effect on SCS. The genetic correlations of fat and protein yields with fat and protein percentages were positive and high,indicating a strong association between these traits. The genetic correlations of milk production traits with SCS were positive and ranged from 0.16 to 0.31. The results showed that SCS is a heritable trait in Valle del Belice sheep and that single-trait selection for increased milk production will also increase SCS

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

New distinguished classes of spectral spaces: a survey

In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The general setting is the space of the semistar operations (of finite type), endowed with a Zariski-like topology, which turns out to be a natural topological extension of the space of the overrings of an integral domain, endowed with a topology introduced by Zariski. One of the key tool is a recent characterization of spectral spaces, based on the ultrafilter topology, given in a paper by C. Finocchiaro in Comm. Algebra 2014. Several applications are also discussed