Polynomial Identities for Bernstein Algebras of Simple Mendelian Inheritance

The Bernstein algebra D n G α of simple Mendelian inheritance is the n-fold duplicate of the gametic algebra G α with basis A 1 ,..., A α and structure constants . We simplify and generalize results of Bernad et al. and Peresi by showing that every identity for G α follows from Costa's shape id...

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Bibliographic Details
Published inCommunications in algebra Vol. 37; no. 10; pp. 3438 - 3455
Main Authors Bremner, Murray R., Piao, Yunfeng, Richards, Sheldon W.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 09.10.2009
Subjects
Algebra
Bernstein algebras
C (programming language)
Computer algebra
Constants
Gallium
Polynomial identities
Primary 17D92
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Secondary 17-04, 17A30, 92D10
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Summary:The Bernstein algebra D n G α of simple Mendelian inheritance is the n-fold duplicate of the gametic algebra G α with basis A 1 ,..., A α and structure constants . We simplify and generalize results of Bernad et al. and Peresi by showing that every identity for G α follows from Costa's shape identity C, and that every identity for the zygotic algebra DG α follows from the recombination identity R. We use computer algebra to determine the identities of degree ≤7 for the copular algebra D 2 G α .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870802502886