A description of a class of finite semigroups that are near to being Malcev nilpotent

In this paper we continue the investigations on the algebraic structure of a finite semigroup $S$ that is determined by its associated upper non-nilpotent graph $\mathcal{N}_{S}$. The vertices of this graph are the elements of $S$ and two vertices are adjacent if they generate a semigroup that is not nilpotent (in the sense of Malcev). We introduce a class of semigroups in which the Mal'cev nilpotent property lifts through ideal chains. We call this the class of \B\ semigroups. The definition is such that the global information that a semigroup is not nilpotent induces local information, i.e. some two-generated subsemigroups are not nilpotent. It turns out that a finite monoid (in particular, a finite group) is \B\ if and only if it is nilpotent. Our main result is a description of \B\ finite semigroups $S$ in terms of their associated graph ${\mathcal N}_{S}$. In particular, $S$ has a largest nilpotent ideal, say $K$, and $S/K$ is a 0-disjoint union of its connected components (adjoined with a zero) with at least two elements

A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS

It was shown by Bergman that the Jacobson radical of a Z-graded ring is homogeneous. This paper shows that the analogous result holds for nil rings, namely, that the nil radical of a Z-graded ring is homogeneous. It is obvious that a subring of a nil ring is nil, but generally a subring of a Jacobson radical ring need not be a Jacobson radical ring. In this paper it is shown that every subring which is generated by homogeneous elements in a graded Jacobson radical ring is always a Jacobson radical ring. It is also observed that a ring whose all subrings are Jacobson radical rings is nil. Some new results on graded-nil rings are also obtained

A longitudinal analysis of the vaginal microbiota and vaginal immune mediators in women from sub-Saharan Africa

In cross-sectional studies increased vaginal bacterial diversity has been associated with vaginal inflammation which can be detrimental for health. We describe longitudinal changes at 5 visits over 8 weeks in vaginal microbiota and immune mediators in African women. Women (N = 40) with a normal Nugent score at all visits had a stable lactobacilli dominated microbiota with prevailing Lactobacillus iners. Presence of prostate-specific antigen (proxy for recent sex) and being amenorrhoeic (due to progestin-injectable use), but not recent vaginal cleansing, were significantly associated with microbiota diversity and inflammation (controlled for menstrual cycle and other confounders). Women (N = 40) with incident bacterial vaginosis (Nugent 7-10) had significantly lower concentrations of lactobacilli and higher concentrations of Gardnerella vaginalis, Atopobium vaginae, and Prevotella bivia, at the incident visit and when concentrations of proinflammatory cytokines (IL-1β, IL-12p70) were increased and IP-10 and elafin were decreased. A higher 'composite-qPCR vaginal-health-score' was directly associated with decreased concentrations of proinflammatory cytokines (IL-1α, IL-8, IL-12(p70)) and increased IP-10. This longitudinal study confirms the inflammatory nature of vaginal dysbiosis and its association with recent vaginal sex and progestin-injectable use. A potential role for proinflammatory mediators and IP-10 in combination with the vaginal-health-score as predictive biomarkers for vaginal dysbiosis merits further investigation

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

A New Wood Preservative

The world owes much to pioneers who blazed the way against many obstacles in teaching wood preservation and conservation, and to the Forestry schools that have been established and to there students who carried on and are still carrying on. Not so many years ago the general opinion held that “there was plenty of wood standing for all time.” Today, conservation of wood is a reality and the world is conserving wood. While much has been done and much is yet being done we find the two old enemies of wood, Fire and Decay, taking an enormous annual toll

Cases, Regulations, and Statutes

<p>ND: not detected (i.e.<0.06 µg/ml lower limit of assay).</p><p>* Hrs post - 1^st dose A, 12^th dose B.</p><p>Median, minimum and maximum values for cervico-vaginal levels of 2G12(µg/ml) after adjustment for dilution factors.</p