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π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented.

π-complemented algebras are defined as those (not necessarily associative or unital) algebras such that each annihilator ideal is complemented by other annihilator ideal. For a given semiprime algebra A, we discuss the π-complementation of the unitisation algebra A 1 of A. Moreover, if in addition the multiplication algebra ℳ(A) of A is also semiprime, we study the π-complementation in the algebras ℳ(A) and ℳ♯(A) (the multiplication ideal of A). In associative setting, we prove that A is π-complemented if and only if ℳ♯(A) is π-complemented, and that A 1 π-complemented if and only if ℳ(A) is π-complemented.

The immune mechanisms underlying the pathogenesis of severe pneumonia associated with the A/H1N1 virus are not well known. The objective of this study was to determine whether severe A/H1N1-associated pneumonia can be explained by the emergence of particular T-cell subsets and the cytokines/chemokines they produced, as well as distinct responses to infection. T-cell subset distribution and cytokine/chemokine levels in peripheral blood and bronchoalveolar lavage (BAL) were determined in patients with severe A/H1N1 infection, asymptomatic household contacts, and healthy controls. Cytokine and chemokine production was also evaluated after in vitro infection with seasonal H1N1 and pandemic A/H1N1 strains. We found an increase in the frequency of peripheral Th2 and Tc2 cells in A/H1N1 patients. A trend toward increased Tc1 cells was observed in household contacts. Elevated serum levels of IL-6, CXCL8, and CCL2 were found in patients and a similar cytokine/chemokine profile was observed in BAL, in which CCL5 was also increased. Infection assays revealed that both strains induce the production of several cytokines/chemokines at 24 and 72 h, however, IL-6, CCL3, and CXCL8 were strongly up-regulated in 72-h cultures in presence of the A/H1N1 virus. Several inflammatory mediators are up-regulated in peripheral and lung samples from A/H1N1-infected patients who developed severe pneumonia. In addition, the A/H1N1 strain induces higher levels of pro-inflammatory cytokines and chemokines than the seasonal H1N1 strain. These findings suggest that it is possible to identify biomarkers of severe pneumonia and also suggest the therapeutic use of immunomodulatory drugs in patients with severe pneumonia associated with A/H1N1 infection.

Let A be an algebra whose multiplication algebra M(A) is semiprime. We prove that, except in an exceptional case, the proper closed prime ideals of A are the maximal closed ideals of A, for the closure operations π and ϵ. In fact, these sets agree for both closures. The same can be said in M(A) for the closure operations π and ϵ′. Moreover, we establish the relationships between the proper closed prime ideals of A and the ones of the algebras M(A),U and A/U, for a given ideal U of A.