Fused Four-Dimensional Real Division Algebras

Dickson's construction obtains the quaternions as pairs of complex numbers with a specific multiplication. We modify his construction to obtain four-dimensional division algebras from pairs of two-dimensional real division algebras and compare this class of algebras to other known classes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31166/1/0000065.pd

Metabolic and anatomic characteristics of benign and malignant adrenal masses on positron emission tomography/computed tomography: a review of literature

PET/CT with (18)F-fluorodeoxyglucose (FDG) or using different radiocompounds has proven accuracy for detection of adrenal metastases in patients undergoing cancer staging. It can assist the diagnostic work-up in oncology patients by identifying distant metastases to the adrenal(s) and defining oligometastatic disease that may benefit from targeted intervention. In patients with incidentally discovered adrenal nodules, so-called adrenal "incidentaloma" FDG PET/CT is emerging as a useful test to distinguish benign from malignant etiology. Current published evidence suggests a role for FDG PET/CT in assessing the malignant potential of an adrenal lesion that has been 'indeterminately' categorized with unenhanced CT, adrenal protocol contrast-enhanced CT, or chemical-shift MRI. FDG PET/CT could be used to stratify patients with higher risk of malignancy for surgical intervention, while recommending surveillance for adrenal masses with low malignant potential. There are caveats for interpretation of the metabolic activity of an adrenal nodule on PET/CT that may lead to false-positive and false-negative interpretation. Adrenal lesions represent a wide spectrum of etiologies, and the typical appearances on PET/CT are still being described, therefore our goal was to summarize the current diagnostic strategies for evaluation of adrenal lesions and present metabolic and anatomic appearances of common and uncommon adrenal lesions. In spite of the emerging role of PET/CT to differentiate benign from malignant adrenal mass, especially in difficult cases, it should be emphasized that PET/CT is not needed for most patients and that many diagnostic problems can be resolved by CT and/or MR imaging