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)
Algebraic structure of genetic inheritance. (English) Zbl 0876.17040

The object of this survey article is to spread one of the most interesting applications of the nonassociative algebra (the genetic algebra) and to present its basis, methods, and recent advances. The author includes a genetic motivation where the necessary language of the biology is introduced. Next, he shows the way in which the genetic information inherited through the generations becomes natural nonassociative algebraic structures. The paper contains a general view of the most important classes of nonassociative algebras with genetic significance (baric algebras, train algebras, Bernstein algebras, ...) which are treated in the following sections. The work finishes with sections devoted to applications and conclusions and an abundant set of references on genetic algebra.

The author remarks in her conclusions that only very few American mathematicians are involved in current work being done in the field and anticipates that “... this article will open an avenue for future discussion and research into this fascinating class of nonassociative algebras and their relationship to the science of genetic inheritance” (sic).

17D92Genetic algebras
17-02Research monographs (nonassociative rings and algebras)
92-02Research monographs (appl. to natural sciences)