Let $p\equiv 1\,(\mathrm{mod}\,9)$ be a prime number and $\zeta_3$ primitive cube root of unity. Then $\mathrm{k}=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$ is pure metacyclic field with group $\mathrm{Gal}(\mathrm{k}/\mathbb{Q})\simeq S_3$. In the case that $\mathrm{k}$ possesses $3$-class $C_{\mathrm{k},3}$ type $(9,3)$, capitulation $3$-ideal classes in its unramified cyclic cubic extensions determine...

We generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field. The normal crossings condition considered by Goward is weakened to the condition that components of the generating divisors meet as complete intersections.

The Defense Mechanism Inventory, a paper and pencil test which purports to measure the relative intensity of usage of five major groups of defenses, is described. The inventory consists of 10 brief stories, two per conflict area, followed by four questions regarding S's actual behavior, fantasy behavior, thoughts, and feelings in the situations described. Five responses typifying the five defen...

a toroidalization of a dominant morphism $varphi: xto y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $x$ and $y$. we give a proof of toroidalization of locally toroidal morphisms of 3-folds.