This note explains consequences of recent work of Frank Quinn for computations of Nil groups in algebraic K-theory, in particular the Nil groups occurring in the K-theory of polynomial rings, Laurent polynomial rings, and the group ring of the infinite dihedral group. 1. Statement of Results Let R be a ring with unit. For an integer q, let KqR be the algebraic K-group of Bass and Quillen. Bass ...

A square matrix is said to be alternating-clean if it is the sum of an alternating matrix and an invertible matrix. In this paper, we determine all alternating-clean matrices over any division ring K. If K is not commutative, all matrices are alternating-clean, with the exception of the 1× 1 zero matrix. If K is commutative, all matrices are alternating-clean, with the exception of odd-size alt...

For a commutative ring R, let Nil(R) be the set of all nilpotent elements of R, Z(R) be the set of all zero divisors of R, T (R) be the total quotient ring of R, and H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R ∈ H, let φ : T (R) −→ RNil(R) such that φ(a/b) = a/b for every a ∈ R and b ∈ R\Z(R). A ring R is called a ZPUI ring if every proper ideal of R...

In this paper we brieƒy discuss Rings — an ecient lightweight library for univariate and multivariate polynomial arithmetic over arbitrary coecient rings. Basic algebra, GCDs and factorization of polynomials are implemented with the use of modern asymptotically fast algorithms. Rings provides a clean API for algebra and a fully typed hierarchy of mathematical structures. Scala API additionall...

Background and Objectives: Surgical site infection (SSI) is the most common nosocomial infection encountered in post operative surgical wards. The use of prophylactic antibiotic in clean elective surgical cases is still a subject of controversy to surgeons. The objective of the study is to identify the need for using prophylactic antibiotics in clean surgeries, prevalence of organisms in patien...

The following theorem is proved: Let R be an algebra with involution over an uncountable field F. Then if the symmetric elements of R are algebraic, R is algebraic. In this paper we consider the following question: "Let R be an algebra with involution over a field F, and assume that the symmetric elements S of R are algebraic over F. Is R algebraic over FT* Previous results related to this ques...

Sitagliptin is a dipeptidyl peptidase-4 (DPP IV, CD26) inhibitor indicated for treatment of Type II diabetes as a second line therapy after metformin. We report fifteen sitagliptin intolerant patients who developed anterior and posterior rhinorrhea, cough, dyspnea, and fatigue. Symptoms typically developed within 1 to 8 weeks of starting, and resolved within 1 week of stopping the drug. Peak ex...