A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

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...

Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.

W. Heisenberg’s famous real matrix group provides a noncommutative translation group of an affine 3-space. The Nil geometry which is one of the eight homogeneous Thurston 3-geometries, can be derived from this matrix group. E. Molnár proved in [2], that the homogeneous 3-spaces have a unified interpretation in the projective 3-sphere PS(V4,V 4,R). In our work we will use this projective model o...

Throughout this paper R denotes an associative ring with identity and all modules are unitary. We use the symbol U(R) to denote the group of units of R and Id(R) the set of idempotents of R, Un(R) the set of elements which are the sum of n units of R, UΣ(R) the set of elements each of which is the sum of finitely many units in R, RE(R) (URE(R)) the set of regular (unit regular) elements of R, a...

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...