In this work, we prove that if a graded, commutative algebra R over a field k is not Koszul, then, denoting by \mathfrak{m} the maximal homogeneous ideal of R and by M a finitely generated graded ...R-module, the nonzero modules of the form \mathfrak{m} M have infinite Castelnuovo-Mumford regularity. We also prove that over complete intersections which are not Koszul, a nonzero direct summand of a syzygy of k has infinite regularity. Finally, we relate the vanishing of the graded deviations of R to having a nonzero direct summand of a syzygy of k of finite regularity.
Differential graded algebra techniques have played a crucial role in the development of homological algebra, especially in the study of homological properties of commutative rings carried out by ...Serre, Tate, Gulliksen, Avramov, and others. In this article, we extend the construction of the Koszul complex and acyclic closure to a more general setting. As an application of our constructions, we shine some light on the structure of the Ext algebra of quotients of skew polynomial rings by ideals generated by normal elements. As a consequence, we give a presentation of the Ext algebra when the elements generating the ideal form a regular sequence, generalizing a theorem of Bergh and Oppermann. It follows that in this case the Ext algebra is noetherian, providing a partial answer to a question of Kirkman, Kuzmanovich, and Zhang.
For each nontrivial semisimple Hopf algebra
H
of dimension sixteen over
ℂ
, the smallest dimension inner-faithful representation of
H
acting on a quadratic AS regular algebra
A
of dimension 2 or 3, ...homogeneously and preserving the grading, is determined. Each invariant subring
A
H
is determined. When
A
H
is also AS regular, thus providing a generalization of the Chevalley–Shephard–Todd Theorem, we say that
H
is a reflection Hopf algebra for
A
.
On the Noether bound for noncommutative rings Ferraro, Luigi; Kirkman, Ellen; Moore, W. Frank ...
Proceedings of the American Mathematical Society,
07/2021, Letnik:
149, Številka:
7
Journal Article
Recenzirano
We present two noncommutative algebras over a field of characteristic zero that each possesses a family of actions by cyclic groups of order 2n, represented in 2 \times 2 matrices, requiring ...generators of degree 3n.
Hypertension is the leading cause of death in developed countries and reduction of salt intake is recommended as a key preventive measure.
To assess the dietary sodium and potassium intakes in a ...national sample of Italian children and adolescents and to examine their relationships with BMI and blood pressure (BP) in the framework of the MINISAL survey, a program supported by the Italian Ministry of Health.
The study population included 1424 healthy subjects (766 boys, 658 girls) aged 6-18 years (mean age: 10.1±2.9) who were consecutively recruited in participating National Health Service centers in 10 Italian regions. Electrolyte intake was estimated from 24 hour urine collections tested for completeness by the concomitant measurement of creatinine content. Anthropometric indices and BP were measured with standardized procedures.
The average estimated sodium intake was 129 mmol (7.4 g of salt) per day among boys and 117 mmol (6.7 g of salt) among girls. Ninety-three percent of the boys and 89% of the girls had a consumption higher than the recommended age-specific standard dietary target. The estimated average daily potassium intakes were 39 mmol (1.53 g) and 36 mmol (1.40 g), respectively, over 96% of the boys and 98% of the girls having a potassium intake lower than the recommended adequate intake. The mean sodium/potassium ratio was similar among boys and girls (3.5 and 3.4, respectively) and over 3-fold greater than the desirable level. Sodium intake was directly related to age, body mass and BP in the whole population.
The Italian pediatric population is characterized by excessive sodium and deficient potassium intake. These data suggest that future campaigns should focus on children and adolescents as a major target in the framework of a population strategy of cardiovascular prevention.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
GOALS:The goal of this study was to evaluate the clinical efficacy of an intake of Lactobacillus salivarius LS01 (DSM 22775) for the treatment of atopic dermatitis (AD) in children.
BACKGROUND:AD is ...an inflammatory and pruritic chronic relapsing skin disorder with multifactorial etiopathology. Some evidence suggests that probiotics may improve AD by modulating the immune system and the composition of intestinal microbiota.
STUDY:A total of 43 patients aged from 0 to 11 years were enrolled in the study (M/F ratio=1:1) and treated with the probiotic strain L. salivarius LS01. Clinical efficacy of probiotic treatment was assessed from baseline by changes in itch index and in the objective SCORAD/SCORAD index.
RESULTS:Patients being given probiotic treatment showed a significant improvement in clinical parameters (SCORAD and itch values) from baseline. The reduction in SCORAD and itch index observed after 4 weeks of treatment also persisted after the cessation of probiotic supplementation.
CONCLUSIONS:L. salivarius LS01 seems to be able to improve the quality of life of children affected by AD and, as a consequence, it may have promising clinical and research implications.
Il C.I.R.B. (Centro Interuniversitario di Ricerca Bioetica), cui aderiscono tutte le Università campane, è un organismo di ricerca nel quale – con metodo rigorosamente scientifico, grazie al concorso ...di qualificati cultori delle varie discipline interessate e in un clima di costante e costruttivo dialogo con i rappresentanti delle diverse posizioni culturali – è possibile delineare le trame di una serena e ponderata riflessione comune su tematiche che coinvolgono l’identità stessa della persona umana e il destino delle generazioni future.
In a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a class of monomial ideals in a polynomial ring, called stable ideals. As a consequence of their construction they deduced ...several homological properties of stable ideals. Furthermore they showed that this resolution admits an associative, graded commutative product that satisfies the Leibniz rule. In this paper we show that their construction can be extended to stable ideals in skew polynomial rings. As a consequence we show that the homological properties of stable ideals proved by Eliahou and Kervaire hold also for stable ideals in skew polynomial rings.
The spread of Covid-19 has worsened the prognosis of oncology patients, interrupting or delaying life-saving therapies and contextually increasing the risk of severe SARS-CoV-2 infections. Acute ...lymphoblastic leukemia (ALL) is the most frequent cancer in pediatric age and the management of this disease with concomitant SARS-COV-2 infection represents a challenging situation.
We present the case of a 6-year-old female newly diagnosed with ALL during a documented SARS-CoV-2 infection. Our patient was admitted 20 days after SARS-CoV-2 detection for evening-rise fever. Laboratory testing showed severe neutropenia while chest x-ray detected moderate pulmonary involvement. Acute lymphoblastic leukemia diagnosis was made through morphological and molecular analysis on bone marrow aspirate. Given the stability of the blood count and clinical conditions, antiviral therapy with Remdesivir and Convalescent Plasma was started before antileukemic treatment, obtaining a rapid resolution of the infection.
In our experience, the treatment with Remdesivir and Convalescent Plasma led to a rapid resolution of Sars-Cov-2 infection. Our case did not present any adverse event to the therapy. Thus, this treatment could be considered in patients with malignancies, in order to accelerate the resolution of the infection and begin immunosuppressive treatment safely. Further studies are required to confirm this hypothesis.
Stable cohomology is a generalization of Tate cohomology to associative rings, first defined by Pierre Vogel. For a commutative local ring R with residue field k, stable cohomology modules ...ExtˆRn(k,k), defined for n∈Z, have been studied by Avramov and Veliche. Stable cohomology carries a structure of Z-graded k-algebra. One of the main goals of this paper is to prove that, for a class of Gorenstein rings, this algebra is a trivial extension of absolute cohomology ExtR(k,k) and a shift of Homk(ExtR(k,k),k). We use this information to characterize the rings R for which stable cohomology is graded-commutative. Stable cohomology is connected through an exact sequence to bounded cohomology. We use this connection to understand the algebra structure of ExtˆR(k,k) by investigating the structure of bounded cohomology Ext‾R(k,k) as a graded ExtR(k,k)-bimodule.
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