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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Algebraic structure of genetic inheritance
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by Mary Lynn Reed PDF
Bull. Amer. Math. Soc. 34 (1997), 107-130 Request permission


In this paper we will explore the nonassociative algebraic structure that naturally occurs as genetic information gets passed down through the generations. While modern understanding of genetic inheritance initiated with the theories of Charles Darwin, it was the Augustinian monk Gregor Mendel who began to uncover the mathematical nature of the subject. In fact, the symbolism Mendel used to describe his first results (e.g., see his 1866 paper Experiments in Plant-Hybridization) is quite algebraically suggestive. Seventy four years later, I.M.H. Etherington introduced the formal language of abstract algebra to the study of genetics in his series of seminal papers [Genetic algebras. Proc. Roy. Soc. Edinburgh, 59:242–258, 1939], [Duplication of linear algebras. Proc. Edinburgh Math. Soc. (2), 6:222–230, 1941.], [Non-associative algebra and the symbolism of genetics. Proc. Roy. Soc. Edinburgh, 61:24–42, 1941.]. In this paper we will discuss the concepts of genetics that suggest the underlying algebraic structure of inheritance, and we will give a brief overview of the algebras which arise in genetics and some of their basic properties and relationships. With the popularity of biologically motivated mathematics continuing to rise, we offer this survey article as another example of the breadth of mathematics that has biological significance. The most comprehensive reference for the mathematical research done in this area (through 1980) is Wörz-Busekros [Algebras in Genetics. Lecture Notes in Biomathematics, vol. 36, Springer-Verlag, New York, 1980].
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Additional Information
  • Mary Lynn Reed
  • Affiliation: Department of Mathematics, Philadelphia College of Pharmacy and Science, Philadelphia, Pennsylvania 19104
  • Address at time of publication: National Security Agency, Ft. George G. Meade, Maryland 20755
  • Email:
  • Received by editor(s): August 1, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 34 (1997), 107-130
  • MSC (1991): Primary 17D92; Secondary 92-02
  • DOI:
  • MathSciNet review: 1414973