Spreads of Right Quadratic Skew Field Extensions
نویسنده
چکیده
~ ABSTRACT. Let L/K be a right quadratic (skew) field extension and let P be a 3-dimensional projective space over K which is embedded in a 3dimensional projective space P over L. Moreover let I be a line of P which ~ carries no point of P. The main result is that even when L or K is a skew ~ field the following holds true: A desarguesian spread of P is given by the ~ ~ set of all lines of P which are indicated by the points of I. A spread of P arises in this way if, and only if, there exists an isomorphism of L onto the kernel of the spread such that K is elementwise invariant. Furthermore a geometric characterization of right quadratic extensions with a left degree other than two and of quadratic Galois extensions is given.
منابع مشابه
BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS
A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...
متن کاملOre extensions of skew $pi$-Armendariz rings
For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...
متن کاملPolynomial Extensions of Skew Fields
An extension L/K of skew fields is called a leftpolynomialextension with polynomial generator 0 if it has a left basis of the form 1, i3, ti’, , Bnm’ for some n. This notion of left polynomial extension is a generalisation of the notion of pseudo-linear extension, known from literature. In this paper we show that any polynomial which is the minimal polynomial over K of some element in an extens...
متن کامل