Journal
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume 50, Issue 5, Pages 1481-1494Publisher
KOREAN MATHEMATICAL SOC
DOI: 10.4134/BKMS.2013.50.5.1481
Keywords
evolution algebra; commutative algebra; isomorphism; nilpotency
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Funding
- PAICYT of Junta de Andalucia (Spain) [FQM143]
- NATO-Reintegration [CBP.EAP.RIG. 983169]
- ICTP [OEA-AC-84]
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The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent n-dimensional complex evolution algebras the possible maximal nilpotency index is 1 + 2(n-1).
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