zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Hypercomplex numbers. An elementary introduction to algebras. Transl. by A. Shenitzer. (English) Zbl 0669.17001
New York etc.: Springer-Verlag. x, 169 p. DM 78.00 (1989).
[For a review of the German translation (Teubner 1978) see Zbl 0395.17001.] The original Russian edition appeared in 1973 as a text-book, intended for students of science high schools. As a matter of fact one cannot expect that this book contains new material and further developments in the study of hypercomplex systems. Nevertheless it was worthwhile to translate it into English because of the lucid way in which the subject is presented by the Russian authors. The book is subdivided into three chapters. The first part deals with the introduction of complex numbers, quaternions and Cayley numbers, presented as hypercomplex number systems and in the third chapter, titled `The exceptional position of four algebras’, it is shown that the number in the “sum of squares” can take on just the four values 1,2,4 and 8 to obtain all division algebras: the reals, the complex numbers, the quaternions and the Cayley algebras. The second part, of an auxiliary nature, is an elementary exposition of the fundamental concepts of linear algebra.
Reviewer: A.H.Boers

17-01Textbooks (nonassociative rings and algebras)
15-01Textbooks (linear algebra)
17A35Division algebras
16KxxDivision rings and semi-simple Artin rings
17D05Alternative rings
16P10Finite associative rings and finite-dimensional algebras
30G35Functions of hypercomplex variables and generalized variables