Year: 1969
Type: article
Abstract: In a recent paper [l], D. A. Foulser described a general construction of finite (left) Veblen-Wedderburn systems which contain the nonexceptional near-fields, the Andre VW systems, the finite Moulton systems, and other new VW systems.At one point in his work Foulser wishes to know whether or not there exist Xsystems of order 26 with kern GF(2).He answers this question in the negative by proving that there is no X-system of order 2d, with kern GF(2), where d = axbv and a, b are primes.At the same time he asks whether or not there exist proper X-systems of order 2d, with kern GF(2), where d contains more than two distinct prime factors.It is the main object of this note to answer this question in the affirmative.More generally we give in §1 a construction of X-systems of order qd, with kern GF(q), where q = p' is an arbitrary power of an arbitrary prime p, and d contains at least three distinct prime factors.In §2 an interesting property of the left and middle nuclei of these X-systems is described.Foulser's notation is, with one exception, followed throughout, and in order to save space this paper cannot be read independently.In particular, it is necessary to have at hand the first two sections plus the first lemma of §5 of Foulser's paper.
Authors: M. L. Narayana Rao, J. L. Zemmer
Institution: University of Missouri
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2042387325