Intermediary rings in normal pairs

Normal Ideals in Regular Rings

Double-normal pairs in space

A double-normal pair of a finite set S of points from R is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair pq is strict if S \ {p, q} lies in the open strip. The problem of estimating the maximum number Nd(n) of double-normal pairs in a set of n points in R, was initiated by Martini and Solt...

On Normal Contact Pairs

We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto’s Theorem on product of almost contact manifolds to flat bundles. We construct some examples on Boothby–Wang fibrations over contact-symplectic manifolds. In p...

Free Symmetric and Unitary Pairs in Division Rings with Involution

Let D be a division ring with an involution and characteristic different from 2. Then, up to a few exceptions, D contains a free pair of symmetric elements provided that (a) it is finite-dimensional and the center has a finite sufficiently large transcendence degree over the prime field, or (b) the center is uncountable, but not algebraically closed in D. Under conditions (a), if the involution...

Normal Ideals of Graded Rings

For a graded domain R = k[X0, ...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal.