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ON THE ALGEBRAIC PROPERTIES OF THE HUMAN ABO-BLOOD GROUP INHERITANCE PATTERN

Part of: Other nonassociative rings and algebras General nonassociative rings

Published online by Cambridge University Press:  21 July 2016

J. M. CASAS Open the ORCID record for J. M. CASAS [Opens in a new window] ,
M. LADRA Open the ORCID record for M. LADRA [Opens in a new window] ,
B. A. OMIROV Open the ORCID record for B. A. OMIROV [Opens in a new window]  and
R. TURDIBAEV Open the ORCID record for R. TURDIBAEV [Opens in a new window]
J. M. CASAS
Affiliation:
Dpto. Matemática Aplicada I, Universidad de Vigo, E. E. Forestal, Campus Universitario A Xunqueira, 36005 Pontevedra, Spain email jmcasas@uvigo.es
M. LADRA*
Affiliation:
Department of Algebra, University of Santiago de Compostela15782, Spain email manuel.ladra@usc.es, rustamtm@yahoo.com
B. A. OMIROV
Affiliation:
Institute of Mathematics, National University of Uzbekistan, Tashkent, 100125, Uzbekistan email omirovb@mail.ru
R. TURDIBAEV
Affiliation:
Department of Algebra, University of Santiago de Compostela15782, Spain email manuel.ladra@usc.es, rustamtm@yahoo.com
*
✉manuel.ladra@usc.es
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Abstract

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We generate an algebra on blood phenotypes with multiplication based on the human ABO-blood group inheritance pattern. We assume that gametes are not chosen randomly during meiosis. We investigate some of the properties of this algebra, namely, the set of idempotents, lattice of ideals and the associative enveloping algebra.

Keywords

Human ABO-blood group inheritanceblood phenotypealgebraabsolute nilpotent elementidempotentsideallatticeassociative algebra

MSC classification

Primary: 17D92: Genetic algebras
Secondary: 17A20: Flexible algebras 92D25: Population dynamics (general)
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 1 , July 2016 , pp. 78 - 95
Copyright
© 2016 Australian Mathematical Society 

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