Centrifiers and ring commutativity

A result of Herstein says in particular that if there exists n > 1 such that xᵑ − x ∈ Z(R) for all x in a ring R then R is commutative. We give an elementary proof of this fact for certain values of n, based on the theory of centrifiers which we develop. For n = 5; 7, we also give an elementary proof of the commutativity of rings R such that xᵑ + x ∈ Z(R) for all x ∈ R

Minimal odd order automorphism groups

We show that 3^7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.Comment: 11 pages, no figures. Manuscript accepted for publicatio

Commuting probability for subrings and quotient rings

We prove that the commuting probability of a finite ring is no larger than the commuting probabilities of its subrings and quotients, and characterize when equality occurs in such a comparison

Counting commutativities in finite algebraic systems

We examine the total possible number of commutativities in a finite algebraic system, concentrating on groups, but also examining rings and semigroups. Numerical restrictions are found and bounds for the total number of commutativities in subgroups and factor groups are derived. Finally, a curious connection with group representations is explored

Boolean rings are definitely commutative!

A ring {R, +, .} is called Boolean if r2 = r for all r ∈ R. We present four proofs that a Boolean ring is commutative

Paracetamol metabolism in postoperative patients

Introduction: Despite being available for more than 50 years, there is still much to learn about paracetamol. Postoperative analgesic regimens that maintain good pain control while minimising exposure to opiates are beneficial and paracetamol has had a resurgence in this role since an IV formulation came to market. However there is evidence to suggest currently licensed doses are sub-therapeutic, especially when administered orally or rectally. Higher, unlicensed doses are now being advocated but, prior to this study, there was little evidence of their safety in surgical patients. When assessing drug safety in surgical patients a number of surgery and patient related factors influence results, and these must be considered. Methods: Major and intermediate surgical patients were recruited from two hospitals in Ireland. They were administered IV paracetamol at either 9g or 4g daily doses. In addition they received daily sub therapeutic doses of four other medicines to indicate the activity of their CYP450 enzymes that are involved in paracetamol metabolism. Urine and blood samples were collected to determine paracetamol pharmacokinetics, CYP450 activity, inflammatory cytokine concentration and for evidence of hepatotoxicity. Results: There were 33 patients that participated in the study. There was no evidence of clinically significant hepatotoxicity occurring in any patient during the study period, but there could have been changes following this time. Paracetamol disposition was shown to change, however half-life remained relatively constant. There were a number of changes to the way paracetamol was metabolised following surgery that maintained this rate of elimination. Conclusion: Doses of up to 9g per day given to major surgical patients for up to five days postoperatively produced no evidence of hepatotoxicity. Further research is warranted to determine the clinical utility of these higher dose

FORMULATION AND OPTIMIZATION OF LEVAMISOLE CHEWABLE TABLETS

Objective: The aim of the present study was to prepare and optimize levamisole chewable tablets by using various super disintegrants, namely; sodium starch glycolate, DRC Indion 204, and DRC Indion 234. Methods: Drug excipient compatibility study was carried out by FTIR spectroscopy to verify the compatibility of levamisole with the excipients. Nine batches of levamisole chewable tablets were prepared according to 32 factorial designs using a direct compression method by optimizing the super disintegrant concentration. The powder blend was exposed to pre-compression studies of the powder blend followed by post-compression studies of the formulated tablets. Results: FTIR study revealed that the excipients used in the formulations were compatible with the drug. The pre-compression and post-compression parameters were found within the IP limits. Form the dissolution studies, it was evident that the formulation prepared with DRC Indion 234 (50 mg) showed maximum percentage drug release in 45 min (97.13%) hence it is considered as optimized formulation. When compared to all other formulation, the batches with DRC Indion 234 (F7-F9) showed a better release of the drug (90 % drug release within 45 min). Conclusion: Nine batches of levamisole chewable tablets were successfully formulated by optimizing the concentration of super disintegrants such as sodium starch glycolate, DRC Indion 204, and DRC Indion 234. It was concluded from the dissolution studies that the DRC Indion 234 is the best super disintegrant irrespective of their concentration for the formulation of levamisole chewable tablets when compared to sodium starch Glycolate and DRC Indion 204